Equation x2 + 5x – 7 = 0 has roots a
and b. Equation 2x2 + px + q = 0 has
roots a + 1 and b + 1. Find p + q.
A. 6
B. o
C. -16
D. 2
Answers
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Answer:
Given: −4 is a root of the equation x
2
+2x+4p=0
Substitute the value of x=−4
(−4)
2
+2(−4)+4p=0
16−8+4p=0
4p=−8
or p=−2
In the quadratic equation x
2
+px(1+3k)+7(3+2k)=0
x
2
−2x(1+3k)+7(3+2k)=0
Compare given equation with the general from of quadratic equation, which ax
2
+bx+c=0
a=1,b=−2(1+3k),c=7(3+2k)
Find Discriminant:
D=b
2
−4ac
=(−2(1+3k))
2
−4×1×7(3+2k)
=4(1+9k
2
+6k)−28(3+2k)
=36k
2
−32k−80
Since roots are real and equal put D=0
36k
2
−32k−80=0
9k
2
−8k−20=0
9k
2
−18k+10k−20=0
9k(k−2)+10(k−2)=0
(k−2)(9k+10)=0
Either, k−2=0 or 9k+10=0
k=2 or k=−10/9
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