Question

find the quadratic equation whose sum and product of zeroes are 4 and 1​

Answer 1

Answer:x x^2-4x+1

Step-by-step explanation:

Every quadratic is of form

K(x^2-(sum of roots )x+product of roots

So the equation would be

(x^2-4x+1)k

Here k can be any constant no.

Answer 2

ANSWER:

• Required quadratic equation => x²-4x+1 = 0

GIVEN:

• α+β = 4
• αβ = 1

TO FIND:

• A quadratic equation.

SOLUTION:

Quadratic equation when roots are given:

=> x²-(α+β)x+αβ = 0. ...(i)

Here:

=> α+β = 4

=> αβ = 1

Putting the values in eq(i) we get;

=> x²-(4)x+1= 0

=> x²-4x+1 = 0

NOTE:

• (a³+b³) = (a+b)(a²+b²-ab)
• (a³-b³) = (a-b)(a²+b²+ab)
• (a+b)² = a²+b²+2ab
• (a-b)² = a²+b²-2ab