Question

if the sum of two root of the quadratic equation is 10 and sum of the square of 2 root is 52 find the quadratic equation please give the answer of this question ​

Answer 1

Solution

Given:-

• the sum of two root of the quadratic equation is 10
• sum of the square of 2 root is 52

Find :-

• Quadratic equations

Explanation

Let,

• First roots be = p
• Second roots be = q

According to question

Case 1.

==> p + q = 10__________(1)

Case 2.

==> p² + q² = 52__________(2)

Squaring both side of equ(1)

==> (p + q)² = 10²

==> p² + q² + 2pq = 100

Keep Value by equ(2)

==> 52 + 2pq = 100

==> 2pq = 100 - 52

==> 2pq = 48

==> pq = 48/2

==> pq = 24

We Have,

$\dag\boxed{\underline{\tt{\red{\:(p-q)\:=\:\sqrt{(p+q)^2-4pq}}}}}$

Keep Values,

==> p - q = √[(10)² - 4×24]

==> p - q = √(100 - 96)

==> p - q = √4

==> p - q = 2___________(3)

Add equ(1) & equ(3)

==> 2p = 12

==> p = 12/2

==> p = 6

Keep in equ(2)

==> 6 - q = 2

==> q = 6 - 2

==> q = 4

Since

• Roots be of Quadratic equation = 6 & 4

Formula of Quadratic Equation

$\dag\boxed{\underline{\tt{\blue{\:x^2-(sum\:of\:roots)x+(product\:of\:roots)\:=\:0}}}}$

Keep all above Values,

==> x² - 10x + 24 =

Hence

• Quadratic Equations will be x² - 10x + 24 = 0

__________________