1.

If (x+3)&(x-4) are the factors of x³+ax²+bx+24, find the values of a&b. With these values of a& b, factorise the given expression ​

Answer»

\large{\underline{\bf{\red{Given:-}}}}

  • ✦ (x + 3) and (x -4 ) are factors of polynomial x³+ax²+bx+24,

\large{\underline{\bf{\red{To\:Find:-}}}}

  • ✦ value of a and b

\huge{\underline{\bf{\pink{Solution:-}}}}

p(x) = x³ + ax² + bx + 24

we know that

(x + 3) and (x -4 ) are factors of the given polynomial.

then,

  • x = -3 or x = 4

putting value of x = -3 in the polynomial.

➝ x³+ax²+bx+24

➝ (-3)³ + a × (-3)² + b ×(-3) +24

➝ -27 + 9a - 3b +24

➝ 9a - 3b -3 =0

Divide both side by 3

we get,

➝ 3a - b -1 = 0 ..........(i)

Now,

putting value of x = 4 in the polynomial.

➝ x³+ax²+bx+24,

➝ (4)³ + a × (4)² + b × (4) +24

➝ 64 +16a + 4B + 24

➝ 16a + 4b + 88 = 0

Divide both side by 4.

we get,

➝ 4A + b + 22 = 0 ..........(ii)

Now , solving equation (i) and (ii)

3a - b = 1

4a + b = -22

7a ⠀⠀= ⠀-21

a⠀⠀⠀ = -21/7

a⠀⠀⠀= -3

putting value of a in equation (i)

we get,

3a - b -1 =0

➝ 3a - b = 1

➝ 3× (-3) - b = 1

➝ -9 - b = 1

➝ - b = 10

➝ b = -10

So, value of a = -3 and b = -10

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