Question

Find the value of k for which the quadratic equation 2x²+ 5x + k =0 has no real roots.

Answer 1

The Following Equation has Real Roots

Hence , Delta = 0 or Delta > 0

Now The Equation

2x² + 5x + k = 0

Now By comparing the equation with ax² + bx + c = 0

We get

a = 2 , b = 5 , c = k

Now ∆ = Delta = b² - 4ac = 0

....According to the question

5² - 4 ( 2) ( k) = 0

25 - 8k = 0

25 = 8k

k = 25/8

Hence the value of K will be 25/ 8

Answer 2

given equation;  2x² + 5x + k = 0

 for no real root

D< 0

D = b -4ac

b²-4ac is less than zero the roots are not real.

 

a=2, b=5, c = k

 

b²-4ac<0

25-4(2)k <0

25-8k <0

-8k < -25

k>25/8  

k>3.125

 

hope so correct and helpful !!!!!!!!!!!!!!!!!!!!!!!