Question

If 1 is the root of the quadratic equation 3x²+an-2=0 and the quadratic equation a(x²+6x)-b=0 has equal roots.Find the value of a and b​

Answer 1

Answer:

It is given that the equation a(x2 + 6x) − b = 0 has equal roots. For roots to be equal, the discriminant of the quadratic equation should be 0. Thus, the value of b is 9.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given :-

1 is the root of the quadratic equation 3x²+ax-2=0 and the quadratic equation a(x²+6x)-b=0 has equal roots.

To find :-

Find the value of a and b ?

Solution :-

Given quardratic equationa are :

3x²+ax-2=0 and a(x²+6x)-b=0

Let p(x) = 3x²+ax-2=0

Let g(x) = a(x²+6x)-b=0

If 1 is the root of the quadratic equation then it satisfies the given equation.

=> p(1) = 0

Now, p(1) = 0

=> 3(1)²+a(1)-2 = 0

=> 3+a-2 = 0

=> 1+a = 0

=> a = -1 -----------(1)

and g(x) = a(x²+6x)-b=0 has equal roots

On Substituting the value of a in g(x)

=> g(x) = (-1)(x²+6x)-b = 0

=> g(x) = -x²-6x-b = 0

=> g(x) = x²+6x+b = 0

On Comparing this with the standard quadratic equation ax²+bx+c=0

a = 1

b=6

c= b

Given that

The equation has equal roots then its discriminant must be equal to zero.

We know that

The discriminant of ax²+bx+c = 0 is D=b²-4ac = 0

=> 6²-4(1)(b)=0

=> 36-4b = 0

=> 36 = 4b

=> 4b = 36

=> b = 36/4

=> b = 9

Therefore, a= -1 and b = 9

Answer:-

The values of a and b for the given problem are -1 and 9 respectively.

Used formulae:-

• If a real number is a root of the given equation then it satisfies the given equation.

• The standard quadratic equation is ax²+bx+c = 0

• The discriminant of ax²+bx+c = 0 is D=b²-4ac

• If D > 0 ,then it has two distinct real roots.

• If D< 0 ,then it has no real roots.

• If D=0,then it has real and equal roots.