Question

Find the zeroes of the quadratic polynomial x2+x-12 and verify the relationship between the zeroes and the coefficients

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given a Quadratic Polynomial x² + x - 12

To Find:

• We have to find the zeros of given polynomial and verify for relation between zeros and Coefficient

Solution:

We have been a Quadratic Polynomial

$\sf{f(x) = x^2 + x - 12}$

We can find the zeros of given Quadratic Polynomial using method of Middle Term Splitting

We need to find two such numbers whose difference is 1 and product is 12

Two such number are 4 and 3

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$\underline{\large\mathfrak\purple{Using \: Middle \: Term \: Splitting }}$

$\implies \sf{x^2 + x - 12 = 0}$

$\implies \sf{x^2 + 4x - 3x - 12 = 0}$

$\implies \sf{x \: (x+4) - 3 \: ( x + 4)=0}$

$\implies \sf{(x+4) \: (x-3) = 0}$

Either

$\implies \sf{x + 4 = 0}$

$\implies \sf{x = -4}$

OR

$\implies \sf{x - 3= 0}$

$\implies \sf{x = 3}$

Hence the zeros of given Quadratic polynomial are -4 and 3

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$\underline{\large\mathfrak\red{Sum \: of \: zeros}}$

$\implies \sf{A + B}$

$\implies \sf{-4+3}$

$\implies \sf{-1 = \left ( - \dfrac{b}{a} \right ) }$

$\underline{\large\mathfrak\red{Product\: of \: zeros}}$

$\implies \sf{A \times B}$

$\implies \sf{-4 \times 3}$

$\implies \sf{-12 = \left ( \: \dfrac{c}{a} \: \right ) }$

Hence the Relation between zeros and Coefficient is verified

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