if -5 is a root of the quadratic equation 2x^2+px-15=0 and the quadratic equation P (x2+x) + k =0 has equal roots, find the value of k.
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For Quadratic Equation 2x^2+px-15
Product Of Roots = -15/2
Implies That, -5×Other Root = -15/2
Other Root = 3/2
Also , Sum Of Roots = -P/2
3/2 -5 = -P/2
-7/2= -P/2
P=7
Now, Since The Roots Of Quadratic Equation Px^2 +P+K = 0 Are Equal
Hence , D =0
P^2-4PK = 0
49-28K=0 [Putting P=7]
K = 49/28
Product Of Roots = -15/2
Implies That, -5×Other Root = -15/2
Other Root = 3/2
Also , Sum Of Roots = -P/2
3/2 -5 = -P/2
-7/2= -P/2
P=7
Now, Since The Roots Of Quadratic Equation Px^2 +P+K = 0 Are Equal
Hence , D =0
P^2-4PK = 0
49-28K=0 [Putting P=7]
K = 49/28
shivamk17:
your answer is wrong...
it should be 140!
-5 Is Not The Root Of 2nd Quadratic Equation . Read The Question Properly , It Says 2nd Quadratic Equation Had Equal Roots
Had = Has
Answered by
1
Answer:
k = 140
Step-by-step explanation:
Given f(x) = 2x² + px - 15 = 0
Given q(x) = p(x² + x) + k = 0.
Given that -5 is a root of f(x).
So,f(-5) = 0
⇒ 2(-5)² + p(-5) - 15 = 0
⇒ 50 - 5p - 15 = 0
⇒ 35 = 5p
⇒ p = 7.
Given that -5 is also root of g(x).
So,g(-5) = 0
⇒ 7[(-5)² - 5] + k = 0
⇒ 7(-5)² + 7(-5) + k = 0
⇒ k = 140.
Therefore,the value of k = 140.
Hope it helps!
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