Question

all the formulas of quadratic equation class 10 (CBSE)
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Answer 1

Answer:

The quadratic equations a1x2 + b1x + c1 = 0 and a2x2 + b2x + c2 = 0 have; One common root if (b1c2 – b2c1)/(c1a2 – c2a1) = (c1a2 – c2a1)/(a1b2 – a2b1) Both roots common if a1/a2 = b1/b2 = c1/c.

Step-by-step explanation:

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Answer 2

Answer:

1. Quadratic Equations

2. Solution by Factorisation

3. Solution by Completing the Square

4. Nature of Roots

Step-by-step explanation:

1. 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.

2. A real number α  is said to be a root of the quadratic equation ax²+bx+c=0,a≠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.

3. 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.

4. The roots of a quadratic equation ax² + bx + c = 0, a≠0 are given by −b±$\sqrt{b^{2}$−4ac2a,provided that b²− 4ac⩾ 0. It is called Quadratic formula.

5. 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.

6. 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

7. Discriminant of the quadratic equation ax² + bx + c = 0, a≠0 is givenby D=b²−4ac.