Question

$3 {x}^{2} - x - 4$
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Answer 1

Question :

Find the zeros of the given quadratic polynomial ; 3x² - x - 4 .

Answer :

x = 4/3 , -1

Solution :

Here ,

The given quadratic polynomial is ;

3x² - x - 4

In order to find the zeros of the given quadratic polynomial , let's equate it to zero .

Thus ,

=> 3x² - x - 4 = 0

=> 3x² - 4x + 3x - 4 = 0

=> x(3x - 4) + (3x - 4) = 0

=> (3x - 4)(x + 1) = 0

=> Either (3x - 4) = 0 or (x + 1) = 0

• If 3x - 4 = 0 , then x = 4/3

• If x + 1 = 0 , then x = -1

Hence ,

x = 4/3 , -1

Answer 2

Answer:

$\huge\rm{Question:–}$

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the co-efficients.

$\huge\rm{\underline{\underline{Solution:–}}}$

$\rm \: ax²+bx+c \\ \rm→a=3;b=-1;c=-4 \\ \rm→Sum \: of \: coefficient= \frac{-b}{a} = \frac{ - ( - 1)}{3} = \frac{1}{3}$

$\rm Product = \frac{c}{a } = \frac{-4}{3}$

$\rm \: → 3x²-x-4 \\ \rm→3x²+3x-4x-4 \\ \rm→3x(x+1)-4(x+1) \\ \rm→(x+1)(3x-4) \\ \rm→x=-1 \: x= \frac{4}{3}$

$\rm \: Sum \: of \: zeroes= \frac{-1}{1} + \frac{4}{3} = \frac{-3+4}{3} = \frac{1}{3}$

$\rm \: Product \: of \: zeroes=(-1) ( \frac{4}{3} )= \frac{-4}{3}$

----» The relationship between zeroes and co-efficients. verified and the values are matching.