Question

if the zeroes of the polynomial x square+px+q are
are double in value to the zeroes of
2x square -5x-3. Find the value of P and Q​

Answer 1

HEY MaTE!

Let us assume the roots of the equation x^2 +px + q are α,β.

Now we find the roots of the equation 2x^2 - 5x - 3.

[Method to find roots is in above image]

Hence, the roots are:- x = 3 or x = -1/2.

Now according to the given data the when the roots of equation

2x^2 -5x -3 = 0 are doubled then we get the roots of the equation x^2 + px + q = 0.

So roots of x^2 + px + q = 0 are :

α = 2(3) β= 2(-1/2)

α = 6. β = -1

Now we form quadratic equation by the following new roots obtained.

=> x^2 - (6+(-1))x -- {6*(-1)}

=> x^2 -5x - 6

Hence the value of p = -5 and of q = -6

Hope it helps

$<marquee><strong><em>HAKUNA</em></strong><strong><em> </em></strong><strong><em>MATATA </em></strong><strong><em>:</em></strong><strong><em>)</em></strong><strong><em>)</em></strong>$

Answer 2

Answer:

HEY MaTE!

Let us assume the roots of the equation x^2 +px + q are α,β.

Now we find the roots of the equation 2x^2 - 5x - 3.

[Method to find roots is in above image]

Hence, the roots are:- x = 3 or x = -1/2.

Now according to the given data the when the roots of equation

2x^2 -5x -3 = 0 are doubled then we get the roots of the equation x^2 + px + q = 0.

So roots of x^2 + px + q = 0 are :

α = 2(3) β= 2(-1/2)

α = 6. β = -1

Now we form quadratic equation by the following new roots obtained.

=> x^2 - (6+(-1))x -- {6*(-1)}

=> x^2 -5x - 6

Hence the value of p = -5 and of q = -6

Step-by-step explanation:

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