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Find the zeros of the following quadratic polynomial and verif

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Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients: 4x2−4x−3.

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Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:

4x2−4x−34x2−4x−3.

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Text solutionVerified

Let

f (x) = 4 x^{2} - 4 x - 3

= 4 x^{2} - (6 x - 2 x) - 3

= 4 x^{2} - 6 x + 2 x - 3

= 2 x (2 x - 3) + 1 (2 x - 3)

= (2 x + 1) (2 x - 3)

To find the zeroes, Let

f (x) = 0

(2 x + 1) (2 x - 3) = 0

2 x + 1 = 0

2 x - 3 = 0

again
sum of zeroes = \dfrac{-1}2 +\dfrac 32 = \dfrac {(-1 +3)}2 = \dfrac 22
=\dfrac {-b}a=\dfrac {(-coefficient \ of \ x)}{( coefficient \ of \ x^2)}

Product of zeroes =\dfrac { -1}{2} \times \dfrac {3}2=\dfrac {(-3)}4
=\dfrac ca
= \dfrac {constant \ term} { coefficient \ of \ x^2 }

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Question Text	Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients: 4x2−4x−3.
Answer Type	Text solution:1
Upvotes	150

Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients: 4x2−4x−34x2−4x−3.

Text solutionVerified

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Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients: 4x2−4x−3.