Q. 134.7( 18 Votes )
If
and x = –3 are the roots of the quadratic equation ax2 + 7x + b = 0 then find the values of a and b.
Answer :
To Find: a and b
Concept Used:
If k is a root of a polynomial f(x), then f(k) = 0
Explanation:
Let f(x) = ax2 + 7x + b = 0
Now,
4a + 42 + 9b = 0
4a + 9b = –42 …..(1)
f(–3) = = a(–3)2 + 7(–3) + b = 0
9a + b – 21 = 0
9a + b = 21….(2)
Multiplying equation (2) by 9, we get,
81a + 9b = 189….(3)
Subtracting equation (1) from equation (3), we get,
81a – 4a + 9b – 9b = 189 – (–42)
77a = 231
a = 3
Putting the value of a in equation 1, we get,
4 × 3 + 9b = –42
12 + 9b = –42
9b = –54
b = –6
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