Question
Mathematics Question on Matrices
The value(s) of k for which the equations x2 - kx - 21 = 0 and x2 - 3kx + 35 = 0 will have a common root is/are
A
(A) k=±4
B
(B) k=±1
C
(C) k=±3
D
(D) k = 0
Answer
(A) k=±4
Explanation
Solution
Explanation:
Let α be the common roots to the equationsx2−kx−21=0 and x2−3kx+35=0∴α2−kα−21=0and α2−3kα+35=0Now by cross multiplication method⇒α=28kFrom (iii) and (iv)28×28k2=49⇒k2=16⇒k=±4