Question

Find the zero of polynomial 2x square+7x-4 is????

Answer 1

Given :

• A polynomial 2x²+7x-4 .

To Find :

• Zeroes of the polynomial 2x²+7x-4 .

Solution :

$\longmapsto\tt\bf{{2x}^{2}+7x-4}$

By Splitting Middle Term :

$\longmapsto\tt{{2x}^{2}+(8x-1x)-4}$

$\longmapsto\tt{{2x}^{2}+8x-1x-4}$

$\longmapsto\tt{2x(x+4)-1(x+4)}$

$\longmapsto\tt{(2x-1)\:(x+4)}$

• x = 1/2
• x = -4

So , 1/2 and -4 are the zeroes of polynomial 2x²+7x-4 ..

_______________________

Here :

• a = 2
• b = 7
• c = -4

Sum of Zeroes :

$\longmapsto\tt{\alpha+\beta=\dfrac{-b}{a}}$

$\longmapsto\tt{\dfrac{1}{2}+\dfrac{-4}{1}=\dfrac{-7}{2}}$

$\longmapsto\tt{\dfrac{1-8}{2}=\dfrac{-7}{2}}$

$\longmapsto\tt\bf{\dfrac{-7}{2}=\dfrac{-7}{2}}$

Product of Zeroes :

$\longmapsto\tt{\alpha\beta=\dfrac{c}{a}}$

$\longmapsto\tt{\dfrac{1}{2}\times\dfrac{-4}{1}=\dfrac{-4}{2}}$

$\longmapsto\tt\bf{\dfrac{-4}{2}=\dfrac{-4}{2}}$

HENCE VERIFIED

Answer 2

2x² + 7x - 4 = 0

By Mid term Splitting,

2x² + 8x - x - 4 = 0

2x(x + 4) -1(x + 4) = 0

( 2x - 1 ) ( x + 4 ) = 0

2x - 1 = 0 and x + 4 = 0

x = 1/2 and x = -4

Hence, the zeroes of polynomial are 1/2 and -4