Question

which number must be added to 4x2 -8x2+3x,so that the resulting polynomial has a factor 2x+1​

Answer 1

$\huge{\underline{\underline{\sf{\pink{Answer:-}}}}}$

let a be added to 4x³ -8x² +3x

then f(x) =4x³ -8x² +3x+a

(2x+1) is a factor of f(z),f(x)=0

now,

2x+1=0

$⟹x = \frac{ - 1}{2}$

$f(x) = 4 {( \frac{ - 1}{2} )}^{3} - 8 {( \frac{ - 1}{2} )}^{2} + 3( \frac{ - 1}{2} ) + a$

$⟹ \frac{ - 1}{2} - 2 - \frac{3}{2} + a = - 4 + a$

so, 2x+1 is a factor

$f( \frac{ - 1}{2} ) = 0$

$⟹ - 4 + a = 0$

$⟹a = 4$

hence 4 must be added