Question

If zeroes of xsquare+PX+q are double in value to the zeroes of 2xsquare-5x-3 then find p and q

Answer 1

Answer:

We have the equation,

$2x^{2} -5x-3=0\\2x^{2} -6x+x-3=0\\(2x+1)(x-3)=0\\i.e,\\x=-1/2 \\or,\\x=3$

Now, the roots of the required equation are double the values respectively.

So, the values of roots of the required quadratic equation will be -1 and 6

Now, the sum of the roots is +5 and the product is -6.

From, the theory of quadratic equations we know that,

sum of roots = -coefficient of x / coefficent of x²

So, -p/1= 5

or

p = -5.

Also, we know that

product of roots = constant term/ coefficient of x²

∴ q/1=-6

or, q = -6

So, the required quadratic equation x²+px+q=0 is x²-5x-6=0.

Hope this helps you !!

Answer 2

Answer:

We have the equation,

2x^{2} -5x-3=0\\2x^{2} -6x+x-3=0\\(2x+1)(x-3)=0\\i.e,\\x=-1/2 \\or,\\x=3

Now, the roots of the required equation are double the values respectively.

So, the values of roots of the required quadratic equation will be -1 and 6

Now, the sum of the roots is +5 and the product is -6.

From, the theory of quadratic equations we know that,

sum of roots = -coefficient of x / coefficent of x²

So, -p/1= 5

or

p = -5.

Also, we know that

product of roots = constant term/ coefficient of x²

∴ q/1=-6

or, q = -6

So, the required quadratic equation x²+px+q=0 is x²-5x-6=0.