Find the equation connecting $a$ and $b$ in order that $2 x^{4} - 7 x^{3} + a x + b$ may be divisible by $x - 3$ .

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Solution

$f (x) = 2 x^{4} - 7 x^{3} + a x + b$
Given that, it is divisible by $x - 3$
Therefore $f (3) = 0$ , we get
$2 (3)^{4} - 7 (3)^{3} + a (3) + b = 0$
$162 - 189 + 3 a + b = 0$
$- 27 + 3 a + b = 0$
$3 a + b = 27$

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Similar questions

Q. If

f (x) = 2 x^{4} - 7 x^{3} + a x + b

is divisible by

(x - 1)

and

(x - 2)

, then

(a, b) =

If the equation $2 x^{4} + 7 x^{3} + a x + b = 0$ has four roots (All real roots) then find the value of a and b. Given that (x - 3) and (x - 1) may exactly divide the above given expression.

Q. Find the conditions that

x^{3} + p x^{2} + q x + r

may be divisible by

x^{2} + a x + b

Q. If the polynomial

7 x^{3} + a x + b

is divisible by

x^{2} - x + 1,

then find the value of

2 a + b

Q. Find the relation between

q

and

r

in order that the equation

x^{3} + q x + r = 0

may be put into the form

x^{4} = (x^{2} + a x + b)^{2}

.
Hence solve the equation

8 x^{3} - 36 x + 27 = 0

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Find the equation connecting a and b in order that 2x4−7x3+ax+b may be divisible by x−3.

f(x)=2x4−7x3+ax+bGiven that, it is divisible by x−3Therefore f(3)=0, we get2(3)4−7(3)3+a(3)+b=0162−189+3a+b=0−27+3a+b=03a+b=27

Find the equation connecting $a$ and $b$ in order that $2 x^{4} - 7 x^{3} + a x + b$ may be divisible by $x - 3$ .

$f (x) = 2 x^{4} - 7 x^{3} + a x + b$
Given that, it is divisible by $x - 3$
Therefore $f (3) = 0$ , we get
$2 (3)^{4} - 7 (3)^{3} + a (3) + b = 0$
$162 - 189 + 3 a + b = 0$
$- 27 + 3 a + b = 0$
$3 a + b = 27$