Home >> Class 10 >> Mathematics >> Important Questions >> Chapter 4
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.
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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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