If the roots of the quadratic equation k x2+27 x +20=0 where k ≠ 0 are in the ratio 4: 5, then find the possible value of ' K '.

Question

If the roots of the quadratic equation k x2+27 x +20=0 where k ≠ 0 are in the ratio 4: 5, then find the possible value of ' K '. (A) 8 (B) 6 (C) 4 (D) 9

Tardigrade Admin · Accepted Answer

Roots are in the ratio 4: 5 Let α=4 P β=5 P Sum of roots α+β =(-b/a) 4 P+5 P =(-27/k) 9 P =(-27/k) P =(-3/k) Product of roots α ⋅ β=(c/a) ⇒(4 P)(5 P)=(20/k) ⇒ 20 P2=(20/k) ⇒((-3/k))2=(1/k) ⇒ (9/k2)=(1/k) ⇒ k=9

Q. If the roots of the quadratic equation kx2+27x +20=0 where k=0 are in the ratio 4:5, then find the possible value of ' K '.

8

6

4

9

Roots are in the ratio 4:5 Let α=4P β=5P Sum of roots α+β=a−b​ 4P+5P=k−27​ 9P=k−27​ P=k−3​ Product of roots α⋅β=ac​ ⇒(4P)(5P)=k20​⇒20P2=k20​ ⇒(k−3​)2=k1​⇒k29​=k1​⇒k=9

Q. If the roots of the quadratic equation $k x^{2} + 27 x$ $+ 20 = 0$ where $k \neq = 0$ are in the ratio $4 : 5$ , then find the possible value of ' $K$ '.