Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i) 14, −1 (ii) √2,13 (iii) 0,√5
(iv) 1,1 (v) −14,14 (vi) 4,1
(i) 14, -1
Using the quadratic equation formula,
x2−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x2−14x−1=0
4x2−x−4=0
(ii) √2,13
Using the quadratic equation formula,
x2−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x2−√2x+13=0
Multiply by 3 to remove denominator,
3x2−3√2x+1=0
(iii) 0, √5
Using the quadratic equation formula,
x2−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x2−0x+√5=0
x2+√5=0
(iv) 1, 1
Using the quadratic equation formula,
x2−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x2−1x+1=0
x2−x+1=0
(v) −14,14
Using the quadratic equation formula,
x2−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x2−−14x+14=0
Multiply by 4
4x2+x+1=0
(vi) 4, 1
Using the quadratic equation formula,
x2−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x2−4x+1=0