Question

if x=0 and x=-1 are the roots of the polynomial. f(x)=2x^3+3x^2+ax+b find a and b​

Answer 1

Answer:

F(0)=0+0+0+b=0

Therefore b=0

F(-1)=-2+3-a+0=0

a=5

Answer 2

$\large\mathrm\red{Given:-}$

• f(x) = 2x³ - 3x² + ax + b

• given Zeroes are 0 and -1

$\large\mathrm\red{To \: find}$

• Value of a and b

$\large\mathrm\red{Solution}$

• value of x = 0 and -1

»Putting x = 0 in the given polynomial

⇢ 2x³ - 3x² + ax + b = 0

⇢ 2×0³ - 3×0² +a×0 + b = 0

⇢ 0 -0 +0 + b = 0

»b = 0

✦ So, we get b = 0

$\large\mathrm\red{Now}$,

»Putting value of x = -1 and b =0 in the given polynomial.

⇢ 2x³ - 3x² + ax + b = 0

⇢ 2×(-1)³ -3 ×(-1)² + a×(-1) + b = 0

⇢ 2× (-1) -3 ×1 -a +0 = 0

⇢ -2 -3 - a = 0

⇢ -5 - a = 0

⇢ - a = 5

» a = -5

$\large\mathrm\red{So}$,

»★Value of a = -5 and b = 0

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