# CBSE Class 10 Answered

**Polynomials. Question from RD Sharma**

The given expression can't be a polynomial, Please use proper + or - signs instead of =.

However you can refer to a similarly answered question, reproduced below,

Query: |

Polynomials |

Query Description: |

if the zeros of the polynomial f(x)= ax^3 + 3bx^2 +3cx + d are in AP prove that 2b^3 -3abc + da^2 = 0 |

Answer: |

Let α, β and γ be the roots or zeros, of the polynomial, ax then we have α + β + γ = -3b/a αβ+ βγ + αγ = 3c/a αβγ = -d/a, Since the roots are in AP, let they be, A-D, A and A+D, where A is a term and D is common difference, then α + β + γ = -3b/a A-D + A + A+D = -3b/a 3A = -3b/a A = -b/a ... (1) Next, αβ+ βγ + αγ = 3c/a (A-D)A + A(A+D) + (A-D)(A+D) = 3c/a A 3A D αβγ = -d/a, (A-D)A(A+D) = -d/a A(A Put for A and D (-b/a)((b (b (b (b (-2b 2b Regards, Team, TopperLearning. |