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Home » Find out which of the following sentences are statements and which are not. Justify your answer. (i) Every rhombus is a square. (ii) x2 + 5|x| + 6 = 0 has no real roots.
Find out which of the following sentences are statements and which are not. Justify your answer. (i) Every rhombus is a square. (ii) x2 + 5|x| + 6 = 0 has no real roots.
CBSE | Class 11 | Exercise 31.1 | Mathematical Reasoning | Maths | RD Sharma
Find out which of the following sentences are statements and which are not. Justify your answer. (i) Every rhombus is a square. (ii) x2 + 5|x| + 6 = 0 has no real roots.

Answers:

(i) Every rhombus is a square.

This sentence is always false, because Rhombuses are not a square.

∴ It is a statement.

(ii) x2 + 5|x| + 6 = 0 has no real roots.

Let us take,

If x>0,

x2+5|x|+6=0

x2+5x+6=0

x = -3 or x = -2

x>0, the equation has no roots.

If x<0,

x2+5|x|+6=0

x2 – 5x+6=0

x<0, the equation has no real roots.

∴ It is a statement.

i

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