Question

find the quadratic polynomial whose zeroes are 2 and -6 also verify the relationship between its coefficient and zeroes.
no need of wrong answer and spam. ​

Answer 1

Answer

• The quadratic polynomial = x² + 4x - 12.

Given

• 2 and -6 are the zeros of the quadratic polynomial.

To Do

• To find the quadratic polynomial and to verify the relationship between its coefficient and zeros.

Step By Step Explanation

In this question we need to find the quadratic polynomial. So let's do it !!

Assumption :

Let us assume that 2 be α and -6 be β.

Formula Used :

$\bigstar \: \: \: \: \underline{\boxed{ \pink{ \bold{{x}^{2} - ( \alpha + \beta)x + \alpha \beta }}}}$

By substituting the values :

Let's substitute the values of α and β to find the quadratic polynomial.

$\longmapsto \sf {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ \\ \longmapsto \sf {x}^{2} - (2 - 6)x +( 2 \times - 6) \\ \\ \longmapsto \sf {x}^{2} - ( - 4)x + ( - 12) \\ \\\longmapsto \underline{ \boxed{\bf{\green{{x}^{2} + 4x - 12}}}} \: \: \: \: \: \dag$

Therefore, the quadratic polynomial = x² + 4x - 12.

Verification

$\bigstar \: \: \: \: \underline{ \boxed{ \red{ \bf{ \alpha + \beta = \cfrac{ - b}{a}}}}} \\ \\ \longmapsto \sf 2 + ( - 6) = \cfrac{ - 4}{1} \\ \\ \longmapsto \underline{\boxed{\bold{ - 4 = - 4}}} \: \: \: \: \dag$

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$\bigstar \: \: \: \: \underline{ \boxed{ \purple{ \bf{\alpha \beta = \cfrac{c}{a}}}}} \\ \\ \longmapsto \sf 2 \times - 6 = \cfrac{ - 12}{1} \\ \\ \longmapsto \underline{ \boxed{ \bold{ - 12 = - 12}}} \: \: \: \: \dag$

Hence, Verified.

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