x² + 4x – 2x²+x² - 10 box- 2
Answers
Step-by-step explanation:
(i) 3x² - 6x + 1 = 0 is a quadratic equation.
(ii) x + (1/x) = 5 is a quadratic equation.
On solving, we get x × x + (1/x) × x = 5 × x
⇒ x
² + 1 = 5x
⇒ x² - 5x + 1 = 0
(iii) √2x² - x - 7 = 0 is a quadratic equation.
(iv) 3x² - √x + 1 = 0 is not a quadratic equation, since the power of x must be a positive integer.
(v) x² - (1/x) + 7 = 0 is not a quadratic equation, since on solving it becomes an equation of degree 3.
(vi) x² - 4 = 0 is a quadratic equation.
(vii) x² = 0 is a quadratic equation.
ax² + bx + c = 0.
● Factorize the quadratic equation.
● Express it as the product of two linear factors, say (px + q) and (rx + s), where p, q, r, S are real numbers and p, r are not equal to zero.
Then, ax² + bx + c = 0
(px + q) (rx + s) = 0
● Put each of the linear factors equal to zero
i.e., px + q = 0 and rx + s = 0
⇒ px = - q ⇒ rx = - s
⇒ x = -q/p ⇒ x = -s/r
● Thus, the two values of x are called the roots of the quadratic equation.
● Therefore, the solution set = {-q/p, -s/r}