Find value of b if root of 2 x square - 3 x + b is equal to zero a given that one of the root is 10 times the other
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Solution :
Let one root = m ,
second root = 10m
Compare given Quadratic equation
2x² - 3x + b = 0 with Ax² + Bx + C = 0 ,
we get
A = 2 , B = -3 , C = b
i ) Sum of the roots = -b/a
=> m + 10m = -b/a
=> 11m = -(-3)/2
=> m = 3/22
Product of the roots = c/a
=> m × 10m = b/2
=> 10m² = b/2
=> b = 20m²
= 20 × ( 3/22 )²
= 20 × 9/484
= 45/121
Therefore ,
b = 45/121
••••
Let one root = m ,
second root = 10m
Compare given Quadratic equation
2x² - 3x + b = 0 with Ax² + Bx + C = 0 ,
we get
A = 2 , B = -3 , C = b
i ) Sum of the roots = -b/a
=> m + 10m = -b/a
=> 11m = -(-3)/2
=> m = 3/22
Product of the roots = c/a
=> m × 10m = b/2
=> 10m² = b/2
=> b = 20m²
= 20 × ( 3/22 )²
= 20 × 9/484
= 45/121
Therefore ,
b = 45/121
••••
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