Exercise 10.2.2

1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

x = −b±b2−4ac2a

(i) x2– 2x – 8

Apply the Quadratic Formula : a=1,b=-2,c=-8.

Then,x1 and x2 are the solution by applying (+)sign and (-) sign.

x1=,x2=.

Sum of Zeroes : ,Product of Zeroes: .

(ii) 4s2 – 4s + 1

Apply the Quadratic Formula : a=4,b=-4,c=1.

Then,s1 and s2 are the solution by applying (+)sign and (-) sign.

s1=,s2=.

Sum of Zeroes : ,Product of Zeroes:/.

(iii) 6x2−3−7x

Apply the Quadratic Formula : a=6,b=-7,c=-3.

Then,x1 and x2 are the solution by applying (+)sign and (-) sign.

x1 = ,x2 = -/.

Sum of Zeroes : /,Product of Zeroes:-.

(iv) 4u2+ 8u

Apply the Quadratic Formula : u1=0,u2=-2.

Then,u1 and u2 are the solution by applying (+)sign and (-) sign.

u1=,u2=.

(v) t2– 15

Apply the Quadratic Formula : t1=+-15

Then,x1 and x2 are the solution by applying with (+)sign and (-) sign.

t1= √15 ,t2= -√15 .

Sum of Zeroes : , Product of Zeroes:.

(vi) 3x2 – x – 4

Apply the Quadratic Formula : a=3,b=-1,c=-6.

Then,x1 and x2 are the solution by applying (+)sign and (-) sign.

x1=1+736, x2=1−736.

Sum of Zeroes : /,Product of Zeroes:.

2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

We know that the general equation of a quadratic polynomial is:

x2 - (sum of roots) x + (product of roots)

(i)14, -1

Substitute the values in quadratic Polynomial: x2-14x+(-1) : x2-14x−1.

(ii)√2 ,13

Substitute the values in quadratic Polynomial:.

(iii) 0, √5

Substitute the values in quadratic Polynomial: : .

(iv) 1, 1

Substitute the values in quadratic Polynomial: x2−1x+1 : x2−x+1.

(v)−14 ,14

Substitute the values in quadratic Polynomial: x2−−14x+14 : x2+14x+14.

(vi) 4,1

Substitute the values in quadratic Polynomial: x2−4x+1.