Question

(1) find the xeroes of each of the following quadratic polynomials and verify the relationship between the zeroes and their co-efficients : 3x^2+10x+7.​

Answer 1

Answer:

Given :-

3x² + 10x + 7

To Find :-

Zeroes

Solution :-

$\sf \: 3 {x}^{2} + 10x + 7$

By splitting middle term

$\sf \: 3 {x}^{2} + (7x + 3x) + 7 = 0$

$\sf \: 3 {x}^{2} + 7x + 3x + 7 = 0$

$\sf \: x(3x + 7) + 1(3x + 7) = 0$

$\sf(3x + 7)(x + 1) = 0$

Value of x are :-

$\sf \: 3x = - 7 \implies \: x = \dfrac{ - 7}{3}$

$\sf \: x = - 1$

Verification

On comparing the equation with ax² + bx + c

a = 3

b = 10

c = 7

$\sf \: \alpha + \beta = \dfrac{ - b}{a}$

$\sf \: - 1 + \bigg( \dfrac{ - 7}{3} \bigg) = \dfrac{ - (10)}{3}$

$\sf \: \dfrac{ - 3 - 7}{3} = \dfrac{ - 10}{3}$

$\sf \: \dfrac{ - 10}{3} = \dfrac{ - 10}{3}$

$\sf \: \alpha \beta = \dfrac{c}{a}$

$\sf \: - 1 \times \dfrac{ -7 }{3} = \dfrac{7}{3}$

$\sf \: \dfrac{7}{3} = \dfrac{7}{3}$

Answer 2

Answer:

Given :-

3x² + 10x + 7

To Find :-

Zeroes

Solution :-

Step-by-step explanation:

see in attachment