- Have any questions?
- [email protected]
- Home
- Let p and q be the roots of the quadratic equation x2– (α – 2)x– α –1 = 0.
Question 1:
Let p and q be the roots of the quadratic equation x2– (α – 2)x– α –1 = 0.What is the minimum possible value of p2 + q2?
A. 0
B. 3
C. 4
D. 5
Feedback We have the equation x2– (α – 2)x– α –1 = 0. its roots are p and q.
So, we have sum of roots = p+q = a–2 and the product of roots, pq = –a –1
Now p2+q2 = (p+q)2 – 2pq = (a–2)2 + 2(a+1)= a2 +4 – 4a + 2a + 2 = (a – 1)2 + 5
Since (α – 1)2 is a perfect square, so its minimum value will be 0, when α = 1.
In that case, the minimum value of p2 + q2will be 5.
So, we have sum of roots = p+q = a–2 and the product of roots, pq = –a –1
Now p2+q2 = (p+q)2 – 2pq = (a–2)2 + 2(a+1)= a2 +4 – 4a + 2a + 2 = (a – 1)2 + 5
Since (α – 1)2 is a perfect square, so its minimum value will be 0, when α = 1.
In that case, the minimum value of p2 + q2will be 5.
These questions are from this test. Would you like to take a practice test?