Question

find the zero of 2x suqare -3+5x and verify the relation ship between the zero and co efficient​

Answer 1

Zeroes are -3/2 and -1 .

Solution:-

We have,

2x² + 3 + 5x

= 2x² + 5x + 3

★ By splitting middle term

= 2x² + 2x + 3x + 3

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

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

The value of 2x² - 3 + 5x is 0 ,

When the value of ( 2x + 3 ) = 0 or ( x + 1 ) = 0

⇒ x = -3/2 or x = -1

Therefore, the zeroes of 2x² + 3 + 5x are -3/2 and 1.

Verification:-

$\star \sf{Sum \: of \: the \: zeroes = \dfrac{ - coefficient \: of \: x }{coefficient \: of \: {x}^{2} } }$

$\rightarrow\sf{ - \dfrac{3}{2} + ( - 1)} = \dfrac{ -5}{2}$

$\rightarrow \sf{ \dfrac{ - 3 - 2}{2} = \dfrac{ - 5}{2} }$

$\rightarrow \bold{ \dfrac{ - 5}{2} = \dfrac{ - 5}{2} }$

$\star\sf{Product \: of \: the \: zeroes = \dfrac{constant \: term}{coefficient \: of \: {x}^{2} } }$

$\rightarrow \sf{ \dfrac{ - 3}{2} \times ( - 1) = \dfrac{3}{2} }$

$\rightarrow \bold{ \dfrac{3}{2} = \dfrac{3}{2} }$