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- The equation ax2 +bx+c, a≠0 is the standard form of a quadratic equation, where a, b and c are real numbers.
ax²+bx+c = 0, a≠ 0 is known as Standard form or General form of a quadratic equation.
In other words, we can say that an equation of order (degree) 2 is called a quadratic equation. - A real number a is said to be a root of the quadratic equation ax² +bx+c = 0, a≠ 0. If aα²+bα+c= 0, the zeroes of quadratic polynomial ax² + bx + c and the roots of the the quadratic equation ax² + bx + c = 0 are the same.
- If we can factorise ax² + bx + c = 0, a≠0 into product of two linear factors, then the roots of the quadratic equation can be found by equating each factors to zero.
- The roots of a quadratic equation ax² + bx + c = 0, a≠0 are given by
x = −b ± √(b2 − 4ac)/2a
provided that b²-4ac≥0. It is called Quadratic formula. - A quadratic equation ax2 + bx + c = 0, a≠ 0 has :
(a) Two distinct and real roots, if b² -4ac>0.
(b) Two equal and real roots, if b² – 4ac =0.
(c) Two roots are not real, if b²-4ac<0. - A quadratic equation can also be solved by the method of completing the square.
(i) a² + 2ab + b² = (a + b)²
(ii) a² – 2ab + b² = (a – b)² - Discriminant of the quadratic equation ax2 + bx + c = 0, a≠0 is given by D=b²-4ac.