Question Text
Question 2 :
State True or False whether the following quadratic equation has two distinct real roots: $\left(x+1\right)\left(x-2\right)+x=0$
Question 3 :
Check whether the following is a quadratic equation: $x^2 + 3x + 1 = (x – 2)^2$
Question 4 :
Check whether the following is quadratic equation : (x - 2)(x +1)=(x - 1)(x + 3)
Question 5 :
Find the roots of the following quadratic equation by factorisation: $x^2 – 3x – 10 = 0$
Question 6 :
State True or False: Every quadratic equation has at least two roots.
Question 7 :
Find the roots of the quadratic equations, if they exist, by the method of completing the square: $4x^2+4\sqrt{3}x+3=0$
Question 8 :
Represent the following situation in the form of quadratic equations: The product of two consecutive positive integers is 306. We need to find the integers.
Question 10 :
Find the roots of the following quadratic equation: $3x^2 – 4\sqrt{3}x + 4 = 0$.
Question 12 :
State true or false:
$b^2 – 4ac$ is called the discriminant of the quadratic equation $ax^2 + bx + c = 0$.
Question 14 :
Justify why the following quadratic equation has no two distinct real roots: $x\left(1-x\right)-2=0$
Question 15 :
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.