If the equations k6x2-3-rx-2x2-1-0 and 6k2x2-1-px-4x2-2-0-k - 0 have both roots common- then the value of pr is

(6k+2)x^2+rx+3k 1=0 ⋯ (1) (12k+4)x^2+px+6k 2=0 ⋯ (2) Since the roots of eqns. (1) and (2) are equal, 6k+212k+4=rp=3k 16k 2 ∴ nbsp;pr=2 ...

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Common Roots

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If the equations $k (6 x^{2} + 3) + r x + (2 x^{2} - 1) = 0$ and $6 k (2 x^{2} + 1) + p x + (4 x^{2} - 2) = 0, k \neq 0$ have both roots common, then the value of $\frac{p}{r}$ is

2

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\frac{1}{2}

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k (6 x^{2} + 3) + r x + (2 x^{2} - 1) = 0

6 k (2 x^{2} + 1) + p x + (4 x^{2} - 2) = 0

\frac{p}{r}

k (6 x^{2} + 3) + r x + (2 x^{2} - 1) = 0

6 k (2 x^{2} + 1) + p x + (4 x^{2} - 2) = 0, k \neq 0

\frac{p}{r}

k (6 x^{2} + 3) + r x + 2 x^{2} - 1 = 0

6 k (2 x^{2} + 1) + p x + 4 x^{2} - 2 = 0

2 r - p

k (6 x^{2} + 3) + r x + 2 x^{2} - 1 = 0 a n d 6 k (2 x^{2} + 1) + p x + 4 x^{2} - 2 = 0

2 r - p

k (6 x^{2} + 3) + r x + (2 x^{2} - 1) = 0

6 k (2 x^{2} + 1) + p x + 4 x^{2} - 2 = 0

2 r - p

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