Question

If one zero of the quadratic polynomial 3x 2 - 10 x – 6k, is reciprocal of the other, find the value of​

Answer 1

Step-by-step explanation:

We know that equation ax

2

+bx+c=0

Then sum of roots =

a

−b

and product of roots=

a

c

Let the other zero be α

Therefore, the other zero is

α

1

Now, α×

α

1

=

a

2

−9

6a

=>1=

a

2

−9

6a

=>a

2

+9−6a=0

=>a

2

−6a+9=0

=>a

2

−3a−3a+9=0

=>a(a−3)−3(a−3)=0

=>(a−3)(a−3)=0

=>a=3 and a=3

Answer 2

Answer:

Given a quadratic equation:2x² – 3x + k

Also given one of the zeros of 2x² – 3x + k is reciprocal to the other,

We need to find the value of k.

Solution

Let us assume that one zeros of the given quadratic equationbe(2x² – 3x + k) be α

Hence the other zero is reciprocal of the zero. So the other zero is 1/α

As per the given equation

a = 2 b = -3 c = k

So, α x 1/α = c/a

1 = k/2

k = 2

The value of k is 2