If one root of the quadratic equation kx2 – 7x + 12 = 0 is 3, then find the value of k.

5. If one root of the quadratic equation kx² – 7x + 12 = 0 is 3, then find the value of k.

Sol. kx² – 7x + 12 = 0

x = 3 is root of given quadratic equation.

So it satisfies the given equation

∴  k(3)² – 7(3) + 12 = 0

∴ k(9) – 21 + 12 = 0

∴ 9k – 9 = 0

∴ 9k = 9

∴ k = 9/9

∴ k = 1

If one root of the quadratic equation x2 - 11x + k = 0 is 9, then find the value of k.

Solution:

The given quadratic equation is x2 – 11x + k = 0

Since  9 is the root of the given quadratic equation

∴ we can put x = 9,

∴ 92 – 11(9) + k = 0

∴ 81 – 99 + k = 0

∴ - 18 + k = 0

∴ k  = 18

∴ the value of k is 18