Question

Find the quadratic equation whose roots are each less by 2 than those of
x2 – 3x +1=0.​

Answer 1

Answer:

x^{2} + x - 1 = 0 is the equation

Step-by-step explanation:

Assume the roots of the equation x^{2}  - 3x + 1=0 (general form-ax^{2}+bx +c) to be p and q

now according to the rules of quadratic equation, the sum of the roots of the equation is -b/a

∴p+q= -(-3)/1 = 3       ...... (equation 1)

and the product of the roots of quadratic equation is c/a

∴p*q=1/1 =1          ........(equation 2)

now as per the condition given,

the sum of the roots of the new equation will be=

(p-2)+(q-2)

=p+q-4

= -1    ......(acco. to equation 1)

the product of the roots of the new equation will be=

(p-2)(q-2)

=p*q -2p -2q + 4

=p*q -2(p+q) +4

=1 -2(3) +4   .......(acco to equation 1 and 2)

= -1

∴the quadratic equation will be,

x^{2} -{(p-2)+(q-2)} +{(p-2)(q-2)}=0

∴x^{2} + x - 1 =0 is the equation.