Question

For what positive value of k, does the . quadratic equation 3x² -kx +3=0 not have real roots?​

Answer 1

$\large{\sf{\underbrace{\orange{Required\:Solution:}}}}$

Given :

• Quadratic equation 3x² - kx +3 = 0 , has no real roots.

On comparing the given with ax² + bx +c = 0, we have :

a = 3, b = -k, c= 3

Then, discriminant, $\displaystyle{\sf{D = b^{2} - 4ac}}$

$\displaystyle{\sf{=(-k) ^{2} - 4\times 3 \times 3}}$

$\displaystyle{\sf{= (-k) ^{2} - 36}}$

But for no real roots, D < 0

Then

k² - 36 < 0

$\implies{\sf{ k^{2} < 36}}$

$\implies{\sf{k< ±6}}$

$\large\implies{\boxed{\sf{\red{k>-6\: or\: k<6}}}}$

Hence, for all O< k<6, the given equation has no real roots.