Question

If a and 3 are the roots of x ^ 2 + 7x + 10 = 0 Find the value of i) (a-B) ii) a² + 3² ili) a²+3²​

Answer 1

Answer:

Given x=−2 is root of equation 3x

2

+7x+p=0

∴x=−2 satisfies the given equation

3(−2)

2

+7(−2)+P=0

12+(−14)+P=0

P=2

The given equation becomes 3x

2

+7x+2=0

3x

2

+6x+x+2=0

3x(x+2)+1(x+2)=0

(3x+1)(x+2)=0

x=

3

−1

or x=−2

Now, x

2

+K(4x+k−1)+P=0

roots are equal

∴D=0D=b

2

−4ac

x

2

+4xk+k

2

−k+2=0

a=1 b=4k C=k

2

−k+2=0

(4k)

2

−4(k

2

−k+2)=0

16k

2

−4k

2

+4k−8=0

12k

2

+4k−8=0

12k

2

+12k−8k−8=0

2k(k+1)−8(k+1)=0

k=

12

8

=

3

2

k=−1.

Step-by-step explanation:

hope it helps