Question 1 :
State True or False whether the following quadratic equation has two distinct real roots: $x^2-3x+4=0$
Question 2 :
Is it possible to design a rectangular mango grove whose length is twice its breadth,and the area is $800 m^2$ ? If so, find its length and breadth.
Question 3 :
Check whether the following is a quadratic equation: $x(x + 1) + 8 = (x + 2) (x – 2)$
Question 5 :
State True or False whether the following quadratic equation has two distinct real roots: $\left(x-1\right)\left(x+2\right)+2=0$
Question 6 :
Find the roots of the following quadratic equation by factorisation: $2x^2 – x + \frac{1}{8} = 0$
Question 7 :
A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Find out at what distances from the two gates should the pole be erected?
Question 8 :
Find the discriminant of the equation $3x^2 – 2x +\frac{1}{3} = 0$.
Question 11 :
Does the following equation has the sum of its roots as 3? $3x^2-3x+3=0$
Question 12 :
Find the roots of the quadratic equation $6x^2 – x – 2 = 0$, by factorisation.
Question 14 :
If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?
Question 15 :
The product of Sunita’s age (in years) two years ago and her age four years from now is one more than twice her present age. What is her present age?
Question 17 :
Represent the following situation in the form of quadratic equations: Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
Question 18 :
A natural number whose square diminished by 84 is equal to thrice of 8 more than the given number is?
Question 19 :
Is it possible to design a rectangular park of perimeter 80 m and area $400 m^2$ ? If so, find its length and breadth.
Question 20 :
State True or False whether the following quadratic equation has two distinct real roots: $2x^2+x-1=0$
Question 21 :
Find the nature of the roots of the quadratic equation $2x^2 – 4x + 3 = 0$.
Question 22 :
Check whether the following is a quadratic equation: $(2x – 1)(x – 3) = (x + 5)(x – 1)$
Question 23 :
Find the roots of the quadratic equations, if they exist, by the method of completing the square: $2x^2 + x + 4 = 0$
Question 24 :
A quadratic equation $ax^2 + bx + c =0$ has two equal real roots when :
Question 25 :
Check whether the following is a quadratic equation: $x^3 – 4x^2 – x + 1 = (x – 2)^3$
Question 27 :
State True or False: If in a quadratic equation, the coefficient of x is zero, then the quadratic equation has no real roots.
Question 28 :
A quadratic equation $ax^2 + bx + c =0$ has no real roots when :
Question 29 :
Find the nature of the roots of the equation $3x^2 – 2x +\frac{1}{3} = 0$.
Question 31 :
Check whether the following is quadratic equation : $x^3 - 4x^2 - x + 1 = (x-2)^3$
Question 34 :
Find the values of k for each of the following quadratic equations, so that they have two equal roots: $2x^2 + kx + 3 = 0$
Question 35 :
Represent the following situation in the form of a quadratic equation : The product of two consecutive positive integers is 306. We need to find the integers.
