Learner Guide : : 15
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lQuadratic polynomial: A polynomial of
degree2
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lQuadratic equation: An equation having
degree 2.
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lGeneral form of a quadratic equation: ax2
+ bx + c = 0, a
≠
0 where a, b, c are real
numbers and x is a variable.
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lRoots of a quadratic equation: Values
of variable which satisfy a quadratic
equation. α is a root of the quadratic equation
ax2 + bx + c = 0, if aα2 + bα + c = 0.
A quadric equation has two roots.
Zeros of a quadratic polynomial and the roots
of the corresponding quadratic equation are the
same.
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lMethods for solution of quadratic equation:
(i) Factor method
(ii) Using the quadratic formula
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lFactor method of solving ax2 + bx + c = 0,
a
≠
0 : Factorise ax2 + bx + c , a
≠
0 into a
product of two linear factors. Equate each
factor to zero and get the values of the variable.
6
QUADRATIC EQUATIONS
These values are the required roots of the given
quadratic equation.
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lQuadratic formula : The roots of the equation
ax2 +bx + c =0 are
2
b b 4ac
2a
− + −
and
2
b b 4ac
2a
− − −
.
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lDiscriminant : The expression b2 – 4ac is called
discriminant of the equation ax2 + bx +c = 0 and
denoted by D.
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lNature of Roots : A quadratic equation
ax2 + bx + c = 0 (a ≠ 0) has
(i) two distinct real roots if D = b2 – 4ac > 0
(ii) two equal (or coincident) and real roots if
D = b2 – 4ac = 0
(iii) no real root if D = b2 – 4ac < 0.
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lWord Problems or daily life problems: To
solve a word problem using quadratic
equations convert the given problem in the form
of a quadratic equation and then solve the
equation by using factor method or quadratic
formula.
CHECK YOUR PROGRESS:
1. Which of the following is not a quadratic equation?
(A) (x - 1) ( x +3 ) = 6 (B)
1
x 7
x
+ =
(C) 3x2 – 5x + 2 = 0 (D) x2 + 2
x
+3 = 0
2. If the quadratic equation 3x2 + mx + 2 = 0 has real and equal roots, then the value of m is :
(A) –
6
(B)
6
(C)
6
2
(D)
±
2 6
3. The discriminant of the quadratic equation 5x2 – 6x – 2 = 0 is :
(A) 56 (B) 66 (C) 76 (D) 86
