Question

Q7.Give the relation(s) between zeroes (a,b) and the coefficients of a quadratic polynomial ax2 + bx + c​

Answer 1

Answer:

Consider quadratic polynomial

P(x) = 2x2 – 16x + 30.

Now, 2x2 – 16x + 30 = (2x – 6) (x – 3)

= 2 (x – 3) (x – 5)

The zeros of P(x) are 3 and 5.

Sum of the zeros = 3 + 5 = 8 = −(−16)2 = -[coefficient of xcoefficient of x2]

Product of the zeros = 3 × 5 = 15 = 302 = [constant term coefficient of x2]

So if ax2 + bx + c, a ≠ 0 is a quadratic polynomial and α, β are two zeros of polynomial then

α+β=−ba

αβ=ca

In general, it can be proved that if α, β, γ are the zeros of a cubic polynomial ax3 + bx2 + cx + d, then

α+β+γ=−ba

αβ+βγ+γα=ca

αβγ=−da

Note: ba, ca and da are meaningful because a ≠ 0.

Answer 2

Q.

Give the relation(s) between zeroes (alpha, beta) and the coefficient of the quadratic polynomial ax² + bx + c

.

Solution -

Sum of zeroes = - b/a

$= > \huge \alpha + \beta = \frac{ - b}{a}$

.

Product of zeroes = c/a

$= > \huge \alpha \beta = \frac{c}{a}$

.

Note :-

Here,

a = coefficient of x²

b = coefficient of x

c = non-variable

hope it helps.