(D) For a quadratic polynomial of the form $ax^2 + bx + c$,the sum of the zeros is given by $-\frac{b}{a}$ and the product of the zeros is given by $\

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(D) For a quadratic polynomial of the form $ax^2 + bx + c$,the sum of the zeros is given by $-\frac{b}{a}$ and the product of the zeros is given by $\frac{c}{a}$.Given the polynomial $3x^2 + x - 4$,we have $a = 3$,$b = 1$,and $c = -4$.Sum of zeros $= -\frac{b}{a} = -\frac{1}{3}$.Product of zeros $= \frac{c}{a} = \frac{-4}{3} = -\frac{4}{3}$.Thus,the sum and product are $-\frac{1}{3}$ and $-\frac{4}{3}$ respectively.

Class 10 Mathematics Polynomials Relationship between Zeroes and Coefficients of a Polynomial

Medium

Obtain the sum and the product of the zeros of the following quadratic polynomial without finding the zeros: $3x^2 + x - 4$.

A
$-\frac{7}{3}, -\frac{5}{3}$
B
$-\frac{9}{3}, -\frac{9}{3}$
C
$-\frac{2}{3}, -\frac{4}{2}$
D
$-\frac{1}{3}, -\frac{4}{3}$

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Obtain the quadratic or the cubic polynomial as the case may be in the standard form with the following coefficients: $a=2, b=3, c=-5, d=0$.

Easy

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Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial:
$t^{3}-2 t^{2}-15 t$

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Find the zeroes of the quadratic polynomial $4s^{2}-4s+1$ and verify the relationship between the zeroes and the coefficients.

Medium

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The product of the zeros of a quadratic polynomial $p(x) = x^{2} + 5x + 6$ is.........

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Find the division of the following by synthetic division method: $p(t) = 2t^2 + 3t + 1$ by $t + 2$.

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Obtain the sum and the product of the zeros of the following quadratic polynomial without finding the zeros: $3x^2 + x - 4$.

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Obtain the quadratic or the cubic polynomial as the case may be in the standard form with the following coefficients: $a=2, b=3, c=-5, d=0$.

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial:$t^{3}-2 t^{2}-15 t$

Find the zeroes of the quadratic polynomial $4s^{2}-4s+1$ and verify the relationship between the zeroes and the coefficients.

The product of the zeros of a quadratic polynomial $p(x) = x^{2} + 5x + 6$ is.........

Find the division of the following by synthetic division method: $p(t) = 2t^2 + 3t + 1$ by $t + 2$.

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Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial:
$t^{3}-2 t^{2}-15 t$