If zeros of x^2 -kx+6 are in the ratio 3:2find k
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Let first root of equation is 3P
and second root is 2P .
sum of roots = -(coefficient of x)/(coefficient of x²) = - (-K)/1 = K
3P + 2P = K
5P = K ------(1)
product of roots =constant/coefficient of x² = 6/1
3P × 2P = 6
6P² = 6
P² = 1 --------(2)
put P value from eqn (1) to eqn (2)
(5/K)² = 1
5² = K²
K = ± 5
hence, value of K = -5 and +5
and second root is 2P .
sum of roots = -(coefficient of x)/(coefficient of x²) = - (-K)/1 = K
3P + 2P = K
5P = K ------(1)
product of roots =constant/coefficient of x² = 6/1
3P × 2P = 6
6P² = 6
P² = 1 --------(2)
put P value from eqn (1) to eqn (2)
(5/K)² = 1
5² = K²
K = ± 5
hence, value of K = -5 and +5
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