The quadratic equation 2x2−48x+q=0 has two roots, where one root is three times greater than the other. What is the value of q?
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Given:
2x²-48x+p=0
Let one root be α and other root(β) be 3α
Here, a= 2, b= - 48,c = p
Sum of zeroes = -b/a
(α +β) = -(-48)/2 = 24
(α +3α) =24
4α = 24
α = 24/4= 6
α= 6
Product of zeroes = c/a
α × β = q/2
α × 3α = q/2 [β=3α]
3α² = q/2
3(6)² = q/2 [α= 6]
36×2× 3 = q
216= q
β=3α
β = 3× 6 = 18
Hence, the value of q= 216 and the two roots are α= 6 , β= 18
HOPE THIS WILL HELP YOU....
2x²-48x+p=0
Let one root be α and other root(β) be 3α
Here, a= 2, b= - 48,c = p
Sum of zeroes = -b/a
(α +β) = -(-48)/2 = 24
(α +3α) =24
4α = 24
α = 24/4= 6
α= 6
Product of zeroes = c/a
α × β = q/2
α × 3α = q/2 [β=3α]
3α² = q/2
3(6)² = q/2 [α= 6]
36×2× 3 = q
216= q
β=3α
β = 3× 6 = 18
Hence, the value of q= 216 and the two roots are α= 6 , β= 18
HOPE THIS WILL HELP YOU....
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