Q.33 If 2 is a root of the quadratic equation 3
2 + − 8 = 0 and the quadratic equation 4
2 −
2 + = 0 has equal roots, find the value of k.
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0
Answer:
ID 6692933260 PASWRD 12345
Answered by
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Step-by-step explanation:
⇒ 3x
2
+px−8=0
Substitute x=2, since 2 is root of equation
⇒ 3(2)
2
+p(2)−8=0
⇒ 12+2p−8=0
⇒ 4+2p=0
∴ p=−2
⇒ 4x
2
−2px+k=0
⇒ 4x
2
−2(−2)x+k=0 [ Since, p=−2 ]
⇒ 4x
2
+4x+k=0
⇒ Here, a=4,b=4,c=k
⇒ It is given that roots are equal.
∴ b
2
−4ac=0
⇒ (4)
2
−4(4)(k)=0
⇒ 16−16k=0
⇒ 16k=16
∴ k=1
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