Question

Question ➡️ Find zeroes and verify the relationship between zeroes and coefficients

4u^2+8u



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Answer 1

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Let 4u² + 8u = 0

4u(u + 2) = 0

4u = 0 or u + 2 = 0

u = 0 or u = -2

sum of the roots = -b/a  = -8/4 = -2

But sum of the roots = 0 + (-2) = -2

Product of the roots = c/a = 0 (As there is no c in the equation)

But, product of the roots = 0 × –2 = 0

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Answer 2

Question

$4{u}^{2} + 8u$

Solution

To find zeroes:

p(u) = 0

$p(u) = 4{u}^{2} + 8u = 0 \\ \implies 4u(u+2) =0 \\ \implies 4u = 0 \:; u + 2 = 0$

4u = 0

u = 0

u + 2 = 0

u = -2

Zeroes of p(u) are 0 and -2

To verify the relationship

Sum of zeroes = -2 + 0 = -2

Product of zeroes = -2 × 0 = 0

Sum of zeroes = $\dfrac{-Coefficient \: of\: u}{Coefficient \:of\: {u}^{2}}$

$= \dfrac{-8}{4} = -2$

Product of zeroes = $\dfrac{Constant\: term}{Coefficient \: of \: {x}^{2}}$

$= \dfrac{0}{4} = 0$

Hence, verified.