{"id":10011,"date":"2019-06-14T01:59:14","date_gmt":"2019-06-13T20:29:14","guid":{"rendered":"https:\/\/www.cbselabs.com\/?page_id=10011"},"modified":"2021-09-18T15:33:01","modified_gmt":"2021-09-18T10:03:01","slug":"rd-sharma-class-10-solutions-chapter-2-polynomials","status":"publish","type":"page","link":"https:\/\/www.cbselabs.com\/rd-sharma-class-10-solutions-chapter-2-polynomials\/","title":{"rendered":"RD Sharma Class 10th Solutions Chapter 2 Polynomials"},"content":{"rendered":"
Question 1. Question 2. Question 3. Question 4. Question 5. Question 6. Question 7. Question 8. Question 9. Question 10. Question 11. Question 12. Question 13. Question 14. Question 15. Question 16. Question 17. Question 18. Question 19. Question 20. Question 21. RD Sharma Class 10 Solutions Chapter 2 Polynomials Ex 2.1<\/p>\n
\nFind the zeros of each of the following quadratic polynomials and verify the relationship between the zeros and their co-efficients :
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\nSolution:
\n(i) f(x) = x2<\/sup>\u00a0– 2x – 8
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\nFor each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorization.
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\nSolution:
\n(i) Given that, sum of zeroes (S) = – \\(\\frac { 8 }{ 3 }\\)
\nand product of zeroes (P) = \\(\\frac { 4 }{ 3 }\\)
\nRequired quadratic expression,
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\nIf \u03b1 and \u03b2 are the zeros of the quadratic polynomial f(x) = x2<\/sup> – 5x + 4, find the value of \\(\\frac { 1 }{ \\alpha } +\\frac { 1 }{ \\beta } -2\\alpha \\beta\\).
\nSolution:
\n<\/p>\n
\nIf \u03b1 and \u03b2 are the zeros of the quadratic polynomial p(y) = 5y2<\/sup> – 7y + 1, find the value of \\(\\frac { 1 }{ \\alpha } +\\frac { 1 }{ \\beta }\\)
\nSolution:
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\n<\/p>\n
\nIf \u03b1 and \u03b2 are the zeros of the quadratic polynomial f(x) = x2<\/sup> – x – 4, find the value of \\(\\frac { 1 }{ \\alpha } +\\frac { 1 }{ \\beta } -\\alpha \\beta\\)
\nSolution:
\n<\/p>\n
\nIf \u03b1 and \u03b2 are the zeros of the quadratic polynomial f(x) = x2<\/sup> + x – 2, find the value of \\(\\frac { 1 }{ \\alpha } -\\frac { 1 }{ \\beta }\\)
\nSolution:
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\n<\/p>\n
\nIf one zero of the quadratic polynomial f(x) = 4x2<\/sup> – 8kx – 9 is negative of the other, find the value of k.
\nSolution:
\n<\/p>\n
\nIf the sum of the zeros of the quadratic polynomial f(t) = kt2<\/sup> + 2t + 3k is equal to their product, find the value of k.
\nSolution:
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\nIf \u03b1 and \u03b2 are the zeros of the quadratic polynomial p(x) = 4x2<\/sup> – 5x – 1, find the value of \u03b12<\/sup>\u03b2 + \u03b1\u03b22<\/sup>.
\nSolution:
\n<\/p>\n
\nIf \u03b1 and \u03b2 are the zeros of the quadratic polynomial f(t) = t2<\/sup> – 4t + 3, find the value of \u03b14<\/sup>\u03b23<\/sup> + \u03b13<\/sup>\u03b24<\/sup>.
\nSolution:
\n<\/p>\n
\nIf \u03b1 and \u03b2 are the zeros of the quadratic polynomial f (x) = 6x4<\/sup> + x – 2, find the value of \\(\\frac { \\alpha }{ \\beta } +\\frac { \\beta }{ \\alpha }\\)
\nSolution:
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\n<\/p>\n
\nIf \u03b1 and \u03b2 are the zeros of the quadratic polynomial p(s) = 3s2<\/sup> – 6s + 4, find the value of \\(\\frac { \\alpha }{ \\beta } +\\frac { \\beta }{ \\alpha } +2\\left( \\frac { 1 }{ \\alpha } +\\frac { 1 }{ \\beta } \\right) +3\\alpha \\beta\\)
\nSolution:
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\n<\/p>\n
\nIf the squared difference of the zeros of the quadratic polynomial f(x) = x2<\/sup> + px + 45 is equal to 144, find the value of p
\nSolution:
\n<\/p>\n
\nIf \u03b1 and \u03b2 are the zeros of the quadratic polynomial f(x) = x2<\/sup> – px + q, prove that:
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\nSolution:
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\n<\/p>\n
\nIf \u03b1 and \u03b2 are the zeros of the quadratic polynomial f(x) = x2<\/sup> – p(x + 1) – c, show that (\u03b1 + 1) (\u03b2 + 1) = 1 – c.
\nSolution:
\n<\/p>\n
\nIf \u03b1 and \u03b2 are the zeros of the quadratic polynomial such that \u03b1 + \u03b2 = 24 and \u03b1 – \u03b2 = 8, find a quadratic polynomial having \u03b1 and \u03b2 as its zeros.
\nSolution:
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\nIf \u03b1 and \u03b2 are the zeros of the quadratic polynomial f(x) = x2<\/sup> – 1, find a quadratic polynomial whose zeros are \\(\\frac { 2\\alpha }{ \\beta }\\) and \\(\\frac { 2\\beta }{ \\alpha }\\)
\nSolution:
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\nIf \u03b1 and \u03b2 are the zeros of the quadratic polynomial f(x) = x2<\/sup> – 3x – 2, find a quadratic polynomial whose zeros are \\(\\frac { 1 }{ 2\\alpha +\\beta }\\) and \\(\\frac { 1 }{ 2\\beta +\\alpha }\\)
\nSolution:
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\n<\/p>\n
\nIf \u03b1 and \u03b2 are the zeroes of the polynomial f(x) = x2<\/sup> + px + q, form a polynomial whose zeros are (\u03b1 + \u03b2)2<\/sup> and (\u03b1 – \u03b2)2<\/sup>.
\nSolution:
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\n<\/p>\n
\nIf \u03b1 and \u03b2 are the zeros of the quadratic polynomial f(x) = x2<\/sup> – 2x + 3, find a polynomial whose roots are :
\n(i) \u03b1 + 2, \u03b2 + 2
\n(ii) \\(\\frac { \\alpha -1 }{ \\alpha +1 } ,\\frac { \\beta -1 }{ \\beta +1 }\\)
\nSolution:
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\nIf \u03b1 and \u03b2 are the zeros of the quadratic polynomial f(x) = ax2<\/sup> + bx + c, then evaluate :
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\nSolution:
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\n<\/p>\nRD Sharma Class 10th Solutions Chapter 2 Polynomials Ex 2.2<\/span><\/h3>\n
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