Question

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) $k=\pm 4$
• (B) $k=\pm 1$
• (C) $k=\pm 3$
• (D) k =  0

Answer 1

The Correct Option is A

Explanation:
Let $\alpha$ be the common roots to the equations$$x^2-kx-21=0\text{ and }{x}^2-3kx+35=0$$$\therefore {\alpha }^2-k\alpha -21=0$and ${\alpha }^2-3k\alpha +35=0$Now by cross multiplication method$$\Rightarrow \alpha =\frac{28}{k}$$From (iii) and (iv)$$\begin{array}{l}\frac{28\times 28}{k^2}=49\\ \Rightarrow k^2=16\\ \Rightarrow k=\pm 4\end{array}$$