In this page equation from roots solution1 we are going to see solution for the worksheet framing quadratic equation from roots.

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

(i) x² – 2 x – 8

Let p(x) = x² – 2 x – 8 = (x-4) (x+2)

So, p(x) = 0

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

x - 4 = 0 x + 2 = 0

x = 4 or x = -2

p (4) = (4 - 4) (x + 2)

= 0

P (-2) = (x - 4) (-2 + 2)

= 0

Hence the zeroes of p(x) are 4 and -2

Thus, Sum of zeroes = 2 and the product of zeroes = -8

From the basic relationships, we get

The sum of the zeroes = -coefficient of x/coefficient of x²

= -(-2)/1

= -2

The product of the zeroes = constant term/coefficient of x²

= -8/1

= -8

Thus, the basic
relationship verified.

(ii) 4 x² – 4 x + 1

Let p(x) = 4 x² – 4 x + 1 = (2 x - 1) (2 x - 1)

So, p(x) = 0

(2 x - 1) (2 x - 1) = 0

2 x – 1 = 0 2 x - 1 = 0

2x = 1 2x = 1

X = 1/2 or x = 1/2

p (1/2) = (2 (1/2) - 1) (2(1/2) - 1)

= (1-1) (1-1)

= 0

p (1/2) = (2 (1/2) - 1) (2(1/2) - 1)

= (1-1) (1-1)

= 0

Hence the zeroes of p(x) are 1/2 and 1/2

Thus, Sum of zeroes = 1 and the product of zeroes = 1/4

From the basic relationships, we get

The sum of the zeroes = -coefficient of x/coefficient of x²

= -(-4)/4

= 1

The product of the zeroes = constant term/coefficient of x²

= 1/4

Thus, the basic relationship
verified.

equation from roots solution1 equation from roots solution1

- Synthetic division
- Rational Expressions
- Rational Zeros Theorem
- LCM -Least Common Multiple
- GCF-Greatest Common Factor
- Simplifying Rational Expressions
- Factorize of Polynomials
- Factoring worksheet
- Framing Quadratic Equation Worksheet
- Remainder Theorem
- Relationship Between Coefficients and roots
- Roots of Cubic equation
- Roots of Polynomial of Degree4
- Roots of Polynomial of Degree5
- System Of Linear Equations

quadratic equation from roots