Question

If 2 and 1 are the two roots of the quadratic equation ax^2 +bx+2=0, find a and b

Answer 1

Answer:

a = 1 & b = -3

Step-by-step explanation:

form the equation with roots

1&2

(x-1)(x-2)=0

=> x²-x-2x+2=0

=>x²-3x+2=0

so we get the ans

Answer 2

Answer:

The values of a and b is $1,-3$.

Step-by-step explanation:

Given 2 and 1 are the roots of the quadratic equation

$ax^{2} +bx+2 = 0$

We have to find the values of a and b.

Here the roots are 2 and 1

so, $x=2 and x=1$

$p(x)= ax^{2} +bx+2$

putting the value of $x = 2$ in the quadratic equation.

$ax^{2} +bx+2=0\\a(2)^{2} +2b+2=0\\4a+2b+2=0$

Divide both side by $2$

$2a+b+1 = 0\\2a+b = -1..............(1)$

Putting the value $x=1$ in the given quadratic equation

$ax^{2} +bx+2=0\\a1^{2} +b(1)+2=0\\a+b+2=0\\a+b = -2.............(2)$

Subtract equation(2) from equation(1)

$2a+b-a-b=-1+2\\a=1$

Putting the value $a=1$ in equation(1)

$2a+b=-1\\2(1)+b=-1\\b=-1-2\\b=-3$

Therefore

$a=1\\b=-3$.