QUADRATIC EQUATION

2.2 GENERAL FORM2.2.1 IDENTIFYING

Exercise 1 : Which of the following are quadratic function

2.3 SOLVING QUADRATIC EQUATIONS2.3.1 Factorization

Exercise 3 : Solve the following by quadratic equation factorization.

2.3.2 Completing the square

Exercise 4: Solve the following quadratic equation by completing the square

2.3.3 Quadratic Formula

Exercise 5 : Solve the following equations by using the quadratic formula

PASS YEAR QUESTIONSSPM 2001. PAPER 1 Q31. Solve the quadratic equation 2x ( x + 3) = (x+4)(1-x). Give your answer correct to four significant figures.

SPM 2003. PAPER 1 Q31. Solve the quadratic equation 2x ( x 4 ) = (1 - x) (x + 2)

SPM 2013, PAPER 1 Q41. It is given that quadratic function x ( x 5) = 4.a) Express the equations in the form of ax2 + bx + c =0b) State the sum of the roots of the equationc) Determine the type of roots of the equation

EXERCISE1. Form the quadratic equation which has roots 2 dan 3.

2.

Form the quadratic equation which has roots 3 dan . Give your answer in the form , where a, b and c are constants

3. Solve the quadratic equation h2 3h + 2 = 2(h 1).

4. Solve the quadratic equation 2x(x 4) = (1 x)(x + 2).Give your answer correct to four significant figures.

.

5. Solve the following quadratic equations by completing the square.a) x2 + 6x -5 = 0b) 3x2 9x +4 = 0

FORMING A QUADRATIC EQUATIONS FROM THE GIVEN ROOTS AND

Notes

If x1 = and x2 = Then ( x ) = 0 and ( x ) = 0( x ) ( x ) = 0x2 x ax + ab = 0x2 (a+b) x + ab = 0

Product of the rootsSum of the roots

Example:

PASS YEAR QUESTIONSSPM 2001 / P1 QUESTION 4

SPM 2002 / P1 QUESTION 4

SPM 2002 / P1 QUESTION 12

Exercise1. Given one of the roots of the quadratic equation x2 + kx +1 = 0 is four times the other root. Determine the values of k.

2. One of the roots of the quadratic equation 2x2 + 8x = 2k + 1 is three times the other root ,where k is a constant. Find the roots and the value of k.Roots: .k = ..

3.

Given that m and n are the roots of the quadratic equation x2 + 3x 9 = 0, form a quadratic equation whose roots are and .

TYPES OF ROOTS QUADRATIC EQUATION

Exercise1. Find the values of h if the equation x2 = 4hx 36

2. The quadratic equation kx2 2(3 + k) x = 1 k has no real roots. Find the range of k

3. Find the range of values of p if the quadratic equation has two distinct roots.

4. The quadratic equation has no roots. Find the range of values of k .

5. The quadratic equation has two distinct roots. Find the rangeof values of p.

6. A quadratic equation has two equal roots. Find the possible values of p.