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Examples 11 and 12

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(11) Find the set of values of k for which 2x² + 20x + k can be factorized into real linear factors.

Soln. 2x² + 20x + k will be factorizable only when D $\geq$ 0.

i.e., 20² – 4 $\times$ 2 $\times$ k $\geq$ 0 or k $\leq$ 25.

(12) If one root of 7x² + 10x + k = 0 be reciprocal of the other, find the value of k.

Soln. Roots are reciprocal $\large \Rightarrow$ a = c $\large \Rightarrow$ 7 = k $\large \Rightarrow$ k = 7