Chapter 4 – Quadratic Equations

1) Solve by factorization

2) By the method of completion of squares show that the equation 4x² + 3x + 5 = 0 has no real roots.

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3) Solve :

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4) Determine the value of for which the quadratic equation 2x² + 3x + k = 0 have both roots real.

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5) Find the roots of the equation 2x² + x – 6 = 0

6) Find the roots of the equation

Ans – x = 3/2

7) A rectangular field has a diagonal of 60 meter more than the shorter side. If, the longer side is 30 meter more than the shorter side, find the sides of the field.

Ans –

Let shorter side of rectangle = x meters

Let diagonal of rectangle = (x + 60) meters

Let longer side of rectangle = (x + 30) meters

According to Pythagoras theorem,

Since we can’t have a negative value for a length we can ignore -30.

=> x = 90, i.e the length of the shorter side is 90 meters,

And length of longer side = x + 30 = 90 + 30 = 120 meters

8) A train travel at same speed for 360 km. For the same distance train would have taken 1 hour less if the speed had been 5 km/hr. more. Calculate the speed of the train.

Ans – Let the speed of the train = x km/hr.

If, the speed had been 5 km/hr more, train would have taken 1 hour less.

Since we can’t have a negative value for speed we can ignore -45.

=> Speed of train = 40 km/hr

9) Find value of x in p²x² + (p² – q²)x – q² = 0

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