If x2-3 x-2 is a factor of x4-a x2-b then the equation whose roots are a- b is A- x2-9 x-20-0B- x2-9 x-20-0C- x2-9 x-20-0D- x 2-9 x -20-0

The correct option is B x^2 9x+20 = 0x^2 3x+2 = (x 1) (x 2) is nbsp; factor of f(x) = x^4 ax^2+b So,nbsp; f(1) = 0 and f(2)= 0 nbsp; ⇒ 1 a+b = 0 nbsp; ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Higher Order Equations

If x2-3 x+2 i...

Question

If $x^{2} - 3 x + 2$ is a factor of $x^{4} - a x^{2} + b$ then the equation whose roots are $a, b$ is

x^{2} - 9 x - 20 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{2} - 9 x + 20 = 0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

x^{2} + 9 x + 20 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{2} + 9 x - 20 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $x^{2} - 9 x + 20 = 0$
$x^{2} - 3 x + 2 = (x - 1) (x - 2)$ is factor of $f (x) = x^{4} - a x^{2} + b$
So, $f (1) = 0 and f (2) = 0$
$\Rightarrow 1 - a + b = 0 and 16 - 4 a + b = 0$
$\Rightarrow a = 5, b = 4$
$∴ Required equation: x^{2} - (5 + 4) x + 5.4 = 0$
$\Rightarrow x^{2} - 9 x + 20 = 0$

Suggest Corrections

Similar questions

Q. The roots of the equation

x^{2} - 9 x + 20 = 0

are

Q. Factorize:

x^{2} - 9 x + 20

Q. (–6, 0), (0, 6) and (–7, 7) are the vertices of a

Δ

ABC. The incircle of the triangle has the equation

Q. If

α, β

are the roots of

x^{2} + 7 x + 5 = 0

, then the equation whose roots are

α - 1, β - 1

Q. Solve:

x^{2} - 9 x + 20 = 0

Join BYJU'S Learning Program

If x2−3x+2 is a factor of x4−ax2+b then the equation whose roots are a,b is

The correct option is B x2−9x+20=0x2−3x+2=(x−1)(x−2) is factor of f(x)=x4−ax2+b So,f(1)=0 and f(2)=0 ⇒1−a+b=0 and 16−4a+b=0 ⇒a=5,b=4 ∴Required equation: x2−(5+4)x+5.4=0 ⇒x2−9x+20=0

If $x^{2} - 3 x + 2$ is a factor of $x^{4} - a x^{2} + b$ then the equation whose roots are $a, b$ is