Question

If = be a solution of the quadratic equation, 2 + 4 + 3 = 0, then value of k is

Answer 1

Answer:

Step-by-step explanation:

Solution (i)  

 

2x2+kx+3=0

 

We know that quadratic equation has two equal roots only when the value of discriminant is equal to zero.

 

Comparing equation  2x2+kx+3=0 with general quadratic equation ax2+bx+c=0, we get

 

a=2,b=k and c=3.

 

Discriminant = b2−4ac=k2−4(2))(3)=k2−24

 

Putting discriminant equal to zero, we get

 

k2−24=0

 

⇒k2=24

 

⇒k=±24−−√=±26–√

 

⇒k=26,−−√−26–√

Answer 2

Answer:

3. If one root of the quadratic equation 2x2 + ax - 6 = 0 is 2, find the value of a. Also, find the other root.

Solution:

Since, x = 2 is a root of the gives equation 2x2 + ax - 6 = 0

⟹ 2(2)2 + a × 2 - 6 = 0

⟹ 8 + 2a - 6 = 0

⟹ 2a + 2 = 0

⟹ 2a = -2

⟹ a = −22

⟹ a = -1

Therefore, the value of a = -1

Substituting a = -1, we get:

2x2 + (-1)x - 6 = 0

⟹ 2x2 - x - 6 = 0

⟹ 2x2 - 4x + 3x - 6 = 0

⟹ 2x(x - 2) + 3(x - 2) = 0

⟹ (x - 2)(2x + 3) = 0

⟹ x - 2 = 0 or 2x + 3 = 0

i.e., x = 2 or x = -32

Therefore, the other root is -32.