Question

if x is equal to 2/3 and X equal to -3 are the roots of the equation ax square + 7 x + b equal to zero find the values of a and b​

Answer 1

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,

f(2/3)² = a(2/3)² + 7 * 2/3+b=0

f(2/3)=4/9a + 14/3+b=0

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

a=3

b= –6

Answer 2

Answer:

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Explanation:

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