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SAI International School
CLASS - X

Mathematics
CHAPTER-4 Quadratic Equations -5

HOME ASSIGNMENT- 5

SUBTOPIC : Nature of Roots

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1 What is the nature of roots of the quadratic equation 4x - 12x - 9 = 0?

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2 What is the nature of the roots of the quadratic equation 2x - 4x + 3 = 0?

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3 For what values of k the quadratic equation kx - 5x + k = 0 has equal roots?

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4 If 2 is a root of the equation x + bx + 12 = 0 and the equation has equal roots,
find the value of b.
5 Write the discriminant of the following quadratic equations.

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6 If the roots of the equation (b - c)x + (c - a)x + (a - b) = 0 are equal, then prove
that 2b = a + c.

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7 Does the quadratic equation 5y - 2y - 2 = 0 have roots? If so, find the roots.
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8 Show that the equation x + ax - 4 = 0 has real and distinct roots for all real values
of a.

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9 Find the set of value(s) of k for which the given polynomial, 4x + kx + 1, can be
factorised into two real linear factors.

Answer:

1 real and unequal roots

2 no real roots

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