Question

Find a quadratic polynomial, whose zeroes are -4 and 3 and verify the relationship between the zeroes and the coefficients.​

Answer 1

$\huge{\bigstar}{ \green{ \mathfrak{ \underline{ \underline{Question}}}}}{\bigstar}$

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Find a quadratic polynomial, whose zeroes are -4 and 3 and verify the relationship between the zeroes and the coefficients.

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$\huge{\bigstar}{ \green{ \mathfrak{ \underline{ \underline{Answer}}}}}{\bigstar}$

☆$\pink{\tt{Let \ zeroes \ are \ \alpha , \ \beta}}$

$\boxed{\red{\bold{Sum \ of \ zeroes:}}}$

$\red{\implies} \alpha + \beta = -4 + 3$

$\red{\implies} \alpha + \beta = -1$

$\boxed{\red{\bold{Product \ of \ zeroes:}}}$

$\purple{\implies} \alpha × \beta = -4 × 3$

$\purple{\implies} \alpha × \beta = -12$

$\boxed{\red{\bold{Now \ the \ polynomial:}}}$

$\green{\implies}x^2 - (\alpha + \beta ) x + (\alpha × \beta)$

$\green{\implies}x^2 - (-1)x + (-12)$

$\green{\boxed{\implies{\boxed{x^2 + x -12}}}}$

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