• If one of the roots of quadratic equation $$\Large 7x^{2}-50x+k=0$$ is 7, then what is the value of k?
 A) 7 B) 1 C) $$\Large \frac{50}{7}$$ D) $$\Large \frac{7}{50}$$

 A) 7

Given equation is $$\Large 7x^{2}-50x+k=0$$

Here, a = 7, b = -50, c = k

Since, $$\Large \alpha + \beta =\frac{-b}{a}$$

Therefore, $$\Large \alpha + \beta =\frac{50}{7}$$

or $$\Large \beta =\frac{50}{7}-7$$

=> $$\Large \beta =\frac{1}{7}$$ [Because $$\Large \alpha = 7$$(given)]

and $$\Large \alpha \beta =\frac{c}{a}$$

or $$\Large 7 \times \frac{1}{7}=\frac{k}{7}$$

k = 7

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