Question

Find zeroes of each of the following polynomials and verify the relationship between the zeroes and its coefficients.
1. 4x^{2}+16x

Answer 1

Answer:

α = 0 , β = -4

Step-by-step explanation:

P(x) = 4x² + 16x

⇒ 4x² + 16x = 0

⇒ 4x ( x + 4 ) = 0

⇒ x = 0 , -4

α = 0 , β = -4

a = 4 , b = 16 , c = 0

Sum of zeroes = -b / a

⇒ 0 - 4 = - 16 / 4

⇒ -4 = -4

Product of zeroes = c / a

⇒ 0( - 4) = 0 / 4

⇒ 0 = 0

Hence verified.

Answer 2

Answer:

$let \: \\ 4 {x}^{2} + 16x = 0 \\ 4x(x + 4) = 0 \\ 4x = 0 \: or \: x + 4 = 0 \\ x = 0 \: and \: x = - 4 \\ \alpha = 0 \: and \: \beta = - 4$

VERIFICATION :-

$\alpha + \beta = - \frac{b}{a} \\ 0 + ( - 4) = - \frac{16}{4} \\ - 4 = - 4 \\ lhs = rhs$

❤️Thank you

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