lf the equations 2x2−7x+1=0 and ax2+bx+2=0 have a common root and a,b are rational, then
A
a=2,b=−7
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B
a=−72,b=1
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C
a=4,b=−14
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D
a=−4,b=1
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Solution
The correct option is Ca=4,b=−14 We have 2x2−7x+1=0⇒x=7±√72−4×22×2=7±√414=irrational And we know that irrational roots of a quadratic occur in pair Hence both the roots of given quadratics have to be common ⇒2a=−7b=12 ∴a=4,b=−14