Question

Find the zeroes of polynomial 5x square +12x +7 and verify relationship b/w zeroes and coefficient of polynomials.​

Answer 1

☸The given polynomial:-

$5x {}^{2} + 12x + 7$

a= 5x^2

b= 12x

c= 7

Factorization~

(by splitting the middle term)

$5x {}^{2} + 12x + 7 \\ =5x {}^{2} + 5x + 7x + 7 \\ = 5x(x + 1) + 7(x + 1) \\ =(5x + 7)(x + 1)$

Zeroes of the polynomial~

$5x + 7 = 0 \\ 5x = - 7 \\ x = \frac{ - 7}{5}$

$x + 1 = 0 \\ x = - 1$

☣Relationship between zeroes and coefficients:-