Question

find the quadratic polynomial, whose addition of zeros is 1/4 and multiplication is -3/4​

Answer 1

Answer:

Quadratic equ.

4x²-x-3 = 0

Step-by-step explanation:

α = 1/4. β = -3/4

quadratic equ.

x²-(α+β)x+αβ = 0

x²-(1/4)x+(-3/4) = 0

4x²-x-3 = 0

Answer 2

Answer:

3/4 and -1

Step-by-step explanation:

let the two zeroes be a and b

a+b=1/4

ab=-3/4

x^2+(a+b)x+ab=0

on substitute the value of a+b and ab in given equation

x^2+(1/4)x+(-3/4)=0

x^2+x/4-3/4=0

Taking LCM of denominators (1,4,4)

We get:

4x^2+x-3÷4=0

on multiply 4 in denominator at LHS to 0 with RHS

we get the equation:4x^2+x-3=0

Now, by the method of spilliting the middle term

we get:

(4x^2+4x)(-3x-3)=0

4x(x+1)-3(x+1)=0

(4x-3)(x+1)=0

4x-3=0 and x+1=0.

4x-3=0.

4x=3

x=3/4

x+1=0

x=-1