If the equation 2x2-x-k-0 and x2-x2-1-0 have 2 common roots then the value of k is-

The correct option is B 2 2x ^ 2 +x+k=0 x ^ 2 + x 2 1=0 have 2 common roots ∴ a _ 1 a _ 2 = b _ 1 b_ 2 = c _ 1 c _ 2 ...

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Byju's Answer

Standard XII

Mathematics

Real Valued Functions

If the equati...

Question

If the equation $2 x^{2} + x + k = 0$ and $x^{2} + \frac{x}{2} - 1 = 0$ have $2$ common roots then the value of $k$ is-

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Solution

The correct option is B $- 2$
${2 x}^{2} + x + k = 0 x^{2} + \frac{x}{2} - 1 = 0 h a v e 2 c o m m o n r o o t s ∴ \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} ∴ \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} \frac{1}{1 / 2} = \frac{k}{- 1} k = - 2$

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If the equation 2x2+x+k=0 and x2+x2−1=0 have 2 common roots then the value of k is-

The correct option is B −22x2+x+k=0x2+x2−1=0have2commonroots∴a1a2=b1b2=c1c2∴b1b2=c1c211/2=k−1k=−2

If the equation $2 x^{2} + x + k = 0$ and $x^{2} + \frac{x}{2} - 1 = 0$ have $2$ common roots then the value of $k$ is-

The correct option is B $- 2$
${2 x}^{2} + x + k = 0 x^{2} + \frac{x}{2} - 1 = 0 h a v e 2 c o m m o n r o o t s ∴ \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} ∴ \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} \frac{1}{1 / 2} = \frac{k}{- 1} k = - 2$