Mathematics exemplar problems class 10 Solutions for Chapter 4 quadratic equations

Which of the following is not a quadratic equation?

Which of the following is a quadratic equation?

Which of the following equations has 2 as a root?

If ½ is a root of the equation x² + kx – 5/4 = 0, then the value of k is

Which of the following equations has the sum of its roots as 3?

Value(s) of k for which the quadratic equation 2x² – kx + k = 0. has equal roots is

(x² + 1)² – x² = 0 has

The quadratic equation 2x^2-\sqrt{5}x+1=0 has

Which of the following equations has no real roots.

Which of the following equations has two distinct real roots?

Which constant must be added and subtracted to solve the quadratic equation 9x^2+\frac{3}{4}x-\sqrt{2}=0 by the method of completing the square?

A statement of Assertion is followed by a statement of Reason is given. Choose the correct answer out of the following choices :

Assertion: Both the roots of the equation ?² – ? + 1 = 0 are real.

Reason: The roots of the equation a?² + b? + c = 0 are real if and only if b² – 4ac ≥ 0.

State whether (x – √2)² – √2(x+1)=0 has real, distinct or equal roots.

State whether x² – 3x + 4 = 0 has real, distinct or equal roots.

State whether 2x² + x – 1 = 0 has real, distinct or equal roots.

State whether 2x² – 6x + (9/2) has real, distinct or equal roots.

State whether 3x² – 4x + 1 = 0 has real, distinct or equal roots.

State whether (x + 4)² – 8x = 0 has real, distinct or equal roots.

State whether √2x² – 3x/√2 + ½ = 0 has real, distinct or equal roots.

Write whether the following statements is true or false.

A quadratic equation with integral coefficient has integral roots.

State whether x (1 – x) – 2 = 0 has real, distinct or equal roots.

Write whether the following statements is true or false. Justify your answer.

If the coefficient of x² and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

State whether (x – 1) (x + 2) + 2 = 0 has real, distinct or equal roots.

State whether (x + 1) (x – 2) + x = 0 has real, distinct or equal roots.

Write whether the following statements is true or false.

Every quadratic equation has at least two roots.

Write whether the following statements is true or false.

Every quadratic equation has exactly one root.

Write whether the following statements is true or false.

Every quadratic equation has at least one real root.

Write whether the following statements is true or false.

Every quadratic equations has at most two roots.

Write whether the following statements is true or false. Justify your answer.

If the coefficient of x² and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.

Is 0.2 a root of equation x² – 0.4 = 0?

Which of the following is a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals?

Does there exist a quadratic equation, whose coefficients are rational both of its roots are irrational? Justify your answer.

If b = 0, c < 0, is it true that the roots of x² + bx + c = 0 are numerically equal and opposite in sign?

Find the roots of 5x² + 13x + 8 = 0.

Find the roots of –3x² + 5x + 12 = 0.

Find the roots of 2 x² – 3x – 5 = 0.

Find the roots of x² + 2 √2x – 6 = 0.

Find the roots of x² – 3 √5x + 10 = 0.

Find the roots of (½)x²– √11x + 1 = 0.

Find the roots of 2x^2+\frac{5}{3}x-2=0.

Find the roots of 3x^2+5\sqrt{5}x-10=0.

Find the roots of 3\sqrt{2}x^2-5x-\sqrt{2}=0.

Find the roots of 21x^2-2x+\frac{1}{21}=0.

Find the roots of \frac{2}{5}x^2-x-\frac{3}{5}=0.

At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.

Find the roots of 8x² + 2x – 3 = 0.

Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number

A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.

A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train(in km/hr).

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(in years)?

In the centre of a rectangular lawn of dimensions 50 m × 40 m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m². Find the length and breadth of the pond.

At t minutes past 2 p.m., the time needed by the minute hand of a clock to show 3 p.m. was found to be 3 minutes less than \frac{t^2}{4} minutes. Find t.

Find the roots of –2x² + 3x + 2 = 0.

Find the roots of 5x² – 2x – 10 = 0.

Find the roots of \frac{1}{(2x-3)}+\frac{1}{(x-5)}=1,x\ne\frac{3}{2},5.

Find the roots of x^2+5\sqrt{5}x-70=0 using quadratic formula.