Question

If the quadratic equation 3x2-4x+k=0
has equal roots, then the value of k is:
O 3/4
Оо
0 -4/3
O 4/3​

Answer 1

EXPLANATION.

Quadratic equation ⇒ 3x² - 4x + k = 0.

As we know that,

D = 0  Or b² - 4ac = 0.

D = discriminant.

⇒ (-4)² - 4(3)(k) = 0.

⇒ 16 - 12k = 0.

⇒ 12k = 16.

⇒ k = 16/12.

⇒ k = 4/3.

Value of k = 4/3.

Option [ D ] is correct answer.

                                                                                                   

MORE INFORMATION.

Nature of the factors of the quadratic equations,

(1) = Real and different, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = imaginary = b² - 4ac < 0.

Answer 2

$\: \: \: \: \: \:{\Large{\bf{\underbrace{Required \: answer}}}}$

${\large{\bold{\rm{\underline{Question}}}}}$

If the quadratic equation 3x² -4x + k = 0 has equal roots, then the value of k is –

(Options are given below –)

• a. 3/4

• b. 0

• c. -4/3

• d. 4/3

${\large{\bold{\rm{\underline{Given \; that}}}}}$

⚕ Quadratic equation is 3x² - 4x + k = 0

${\large{\bold{\rm{\underline{To \; find}}}}}$

⚕ Value of k

${\large{\bold{\rm{\underline{Solution}}}}}$

⚕ Value of k = 4/3 ; Option d.

${\large{\bold{\rm{\underline{Full \; solution}}}}}$

✴ Quadratic equation is 3x² - 4x + k = 0

✴ Value of k = ?

✴ Therefore, discriminant = b² - 4ac

Henceforth,

⇢ (-4)² -4(3)(k)

⇢ (-4)² -4 × 3 × k

⇢ -16 -12 × k

⇢ -16 -12k

✯ Here, the roots are equal..!

✴ Therefore, discriminant be 0

⇢ -16 -12k = 0

⇢ 12k = 0 + 16

⇢ 12k = 16

⇢ k = 16/12

⇢ k = 4/3

• Henceforth, 4/3 is the value of k in quadratic equation 3x² -4x + k = 0