Find k for which the given quadratic equation 9 x^{2}+3 k x+4=0 hasdis

1.	Find k for which the given quadratic equation 9 x^{2}+3 k x+4=0 hasdistinct roots.
Answer» Given quadratic equation is = 9x² + 3kx + 4 = 0 On comparing with standard form of quadratic equation i.e ax² + bx + c =0,a≠0Here, a = 9 , b= 3k, c= 4 D(discriminant)= b²-4ac = (3k)² - 4× 9 ×4= 9k² - 144 Since, roots of given equation are distinct. D > 0. 9k² - 144 > 09(k² - 16) >0(k² - 16) >0 (9≠0)k² -4²>0(k-4) (k+4) >0[ a² - b² = (a-b)(a+b)] k > 4 and k< -4 Hence, the value of k is k > 4 and k< -4.

Find k for which the given quadratic equation 9 x^{2}+3 k x+4=0 hasdistinct roots.

Answer»

Given quadratic equation is = 9x² + 3kx + 4 = 0

On comparing with standard form of quadratic equation i.e ax² + bx + c =0,a≠0Here, a = 9 , b= 3k, c= 4

D(discriminant)= b²-4ac

= (3k)² - 4× 9 ×4= 9k² - 144

Since, roots of given equation are distinct. D > 0.

9k² - 144 > 09(k² - 16) >0(k² - 16) >0 (9≠0)k² -4²>0(k-4) (k+4) >0[ a² - b² = (a-b)(a+b)]

k > 4 and k< -4

Hence, the value of k is k > 4 and k< -4.