Question

Find the quadratic equation whose roots is 2 - root 5

Answer 1

Answer:

Step-by-step

If the roots are 2 and 5

Then

(x-2), (x-5)

The quadratic equation is

x²-7x+10

Answer 2

Question:-

The roots of a quadratic equation are 5 and -2. find the equation.

To Find:-

Find the equation.

Given:-

The roots of the equation are 5 and -2.

Solution:-

Formula Used:-

$\sf\implies\boxed { {x}^{2} - ( \alpha + \beta )x \: + \alpha \beta = 0 }$

Substitute Values:-

• The value of α is 5.
• The value of β is -2.

$\tt\implies \: { x }^{ 2 } - [ 5 + ( -2 ) ]x + ( 5 )( -2 ) = 0$2

$\tt\implies \: { x }^{ 2 } - ( 5 - 2 )x + ( -10 ) = 0$

$\tt\implies \: { x }^{ 2 } - 3x - 10 = 0$

Verification:-

Substitute x = 5:-

$\tt\implies \: { x }^{ 2 } - 3x - 10 = 0$

$\tt\implies \: { 5 }^{ 2 } - 3( 5 ) - 10 = 0$

$\tt\implies \: 25 - 15 - 10 = 0$

$\tt\implies \: 25 - 25 = 0$

$\tt\implies \: 0 = 0$