Question

For what value of k the quadratic equation x² - 3x + k = 0 has two real and equal roots?​

Answer 1

Step-by-step explanation:

b^2-4ac=0

9-4k=0

9=4k

k=9/4

Answer 2

SOLUTION

GIVEN

The quadratic equation x² - 3x + k = 0 has two real and equal roots

TO DETERMINE

The value of k

EVALUATION

Here the given Quadratic equation is

x² - 3x + k = 0

Comparing with the general equation

ax² + bx + c = 0 we get

a = 1 , b = - 3 , c = k

Since the given Quadratic equation has two real and equal roots

$\displaystyle \sf{ \implies Discriminant = 0 }$

$\displaystyle \sf{ \implies {b}^{2} - 4ac = 0 }$

$\displaystyle \sf{ \implies {( - 3)}^{2} - 4 \times 1 \times k = 0 }$

$\displaystyle \sf{ \implies 9 - 4k= 0 }$

$\displaystyle \sf{ \implies - 4k= - 9 }$

$\displaystyle \sf{ \implies k= \frac{9}{4} }$

FINAL ANSWER

$\displaystyle \sf{ k = \frac{9}{4} }$

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