Find the value of b - R such that x2-b x-1-0- x2-x-b-0 have a common root-A- 0 B- i -3C- -i -3D- none of these

The correct option is A x^2 + bx 1 = 0 ................(1) x^2 + x +b = 0 .................(2) Let the common root = α α^2/b^2+1 = α/b+1 1/1 b α = b^2+1/b+1 ...

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Byju's Answer

Standard XII

Mathematics

Condition for Coplanarity of Four Points

Find the valu...

Question

Find the value of b $ϵ R$ such that $x^{2} + b x - 1 = 0, x^{2} + x + b = 0$ have a common root.

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Solution

The correct option is A

$x^{2} + b x - 1 = 0$ ................(1)

$x^{2} + x + b = 0$ .................(2)

Let the common root = $α$

$\frac{α^{2}}{b^{2} + 1}$ = $\frac{α}{b + 1}$ $\frac{1}{1 - b}$

$α = \frac{b^{2} + 1}{b + 1}, α$ = $\frac{1}{1 - b}$

$\frac{b^{2} + 1}{b + 1}$ = $\frac{b + 1}{1 - b}$

$b^{2} + - b^{3} - b$ = $b^{2} + 1 + 2 b$

$b^{3} + 3 b = 0$

$b (b^{2} + 3) = 0$

$b = 0 o r b \neq i \sqrt{3}$

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Find the value of b ϵR such that x2+bx−1=0,x2+x+b=0 have a common root.

The correct option is A x2+bx−1=0 ................(1) x2+x+b=0 .................(2) Let the common root = α α2b2+1 = αb+1 11−b α=b2+1b+1, α = 11−b b2+1b+1 = b+11−b b2+−b3−b = b2+1+2b b3+3b=0 b(b2+3)=0 b=0orb≠ i√3

Find the value of b $ϵ R$ such that $x^{2} + b x - 1 = 0, x^{2} + x + b = 0$ have a common root.