X 2- a 2 x - b -0 and x 2- x -1-0 have a common roots which of the following is true-A- 1-b2-a2-b21-a2B- 1-b2-b2-a1-a2C- 1-b2-a2-b1-a2D- 1-b2-a2-b1-a2

The correct option is D Let the common root = α (1)α^2/a^2 b = (2)α/1 b =(3)1/1 α^2 [ 1 amp; a^2 amp; b 1 amp; 1 amp; 1 ] α = a^2 b/1 b, α = 1 ...

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Byju's Answer

Standard XI

Mathematics

Middle Terms

x 2+ a 2 x + ...

Question

$x^{2} + a^{2} x + b = 0 a n d x^{2} + x + 1 = 0$ have a common roots which of the following is true.

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Solution

The correct option is D

Let the common root = $α$

$\frac{α^{2}}{a^{2} - b} (1)$ = $\frac{α}{1 - b} (2)$ = $\frac{1}{1 - α^{2}} (3)$ $\begin{matrix} 1 & a^{2} & b 1 & 1 & 1 \end{matrix}$

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

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

$(1 - b^{2})$ = $(a^{2} - b) (1 - a^{2})$

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x2+a2x+b=0 and x2+x+1=0 have a common roots which of the following is true.

The correct option is D Let the common root = α α2a2−b(1) = α1−b(2) =11−α2(3) 1a2b111 α = a2−b1−b,α = 1−b1−a2 a2−b1−b = 1−b1−a2 (1−b2) = (a2−b)(1−a2)

$x^{2} + a^{2} x + b = 0 a n d x^{2} + x + 1 = 0$ have a common roots which of the following is true.