Q. 2

Find the value of

Answer :

Given: quadratic equation kx2 - 14x + 8 = 0, one of its root is 2


To find: the value of ‘k’


Explanation: Given 2 is the root of the given equation hence the 2 must satisfy the given equation.


So now putting x = 2 in the given equation, we get


kx2 - 14x + 8 = 0


k(2)2 - 14(2) + 8 = 0


4k - 28 + 8 = 0


4k - 20 = 0


4k = 20


k = 5


Hence the value of k is 5.


OR


Given: quadratic equation x2 + 5kx + 16 = 0, it has real and equal roots


To find: the value of ‘k’


Explanation: The given quadratic equation has real and equal roots, so its determinant will be equal, i.e.,


D = 0


But we know determinant is b2 - 4ac


Hence for real and equal roots, we get


b2 - 4ac = 0………..(i)


Now comparing the given quadratic equation x2 + 5kx + 16 = 0


With the standard quadratic equation ax2 - bx + c = 0, we get


a = 1, b = 5k, c = 16


Substituting these values in equation (i), we get


b2 - 4ac = 0


(5k)2 - 4(1)(16) = 0


25k2 - 64 = 0


25k2 = 64



Taking square root on both sides, we get




Hence the value of k is


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