Study the equation x2 + 10x = -2 and write answers to the
following questions in your own words:
(a) Is this a quadratic equation? Why?
(b) Can you solve this equation by the method of
factorisation? Give reason.
(c) Is the left hand side of the equation a perfect square?
Which term should be added to make it a perfect square?
Answers
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(a) Yes, it is a quadratic equation.
(b) NO, it is not factorisable.
(c) 25 is added to make a perfect square.
The given equation is x² + 10x = - 2
(a) The general quadratic equation is expressed as ax² + bx +c = 0
Comparing the general expression with the given expression of x² + 10x + 2 = 0, we get
a = 1, b = 10, c = 2
So, this is a quadratic equation.
(b) x² + 10x + 2 = 0 cannot be put into factors because the expression is not factorable with rational numbers.
(c) The LHS. is x² + 10x. If we add 25 to it then,
x² + 10x + 25
= (x+5)²
becomes a perfect square.
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