Question

if x= 0 and x=-1 are zeros of the polynomial p(x)=2x^3-3x^2+ax+b, find a and b
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Answer 1

Answer:

• a = -5
• b = 0

★ Given :-

• x = 0 and x = (-1) are zeros of the polynomial p(x)=2x^3-3x^2+ax+b

★ To Find :-

• value of a
• value of b

★ Solution :-

As, x = 0 is zero of the polynomial we can write it as,

$\sf \: p(x) = 0$

Therefore,

$\sf \: p(x)=2x^3-3x^2+ax+b \: = 0$

(when x = 0)

$\implies\sf \: 2(0)^3-3(0)^2+a(0)+b = 0$

$\implies \: \sf \: 0-0+0+b = 0$

$\implies \: \sf { \boxed{\therefore{ \red{ \sf \: b = 0}}}}$

As x = (-1) is another zero of the polynomial we can write,

$\sf \: p(x)=2x^3-3x^2+ax+b \: = 0$

Putting x = (-1) we get,

$\implies \sf \: 2( - 1)^3-3( - 1)^2+a( - 1)+b = 0$

( Putting the value of b we get,)

$\implies \sf \: - 2 - 3 - a + 0 = 0$

$\implies \sf - 5 - a = 0$

$\implies \sf - a = + 5$

$\implies{ \boxed{ \red {\sf a = - 5}}}$

Therefore, the value of a = (-5) and b = 0.