# Quadratic Equation Practice Problem 1

## The roots of the quadratic equation ( a + b -2c )x² – ( 2a – b – c)x +( a – 2b + c) = 0 are-

A. (a + b + c ) and (a – b- c)

B.  $$\frac{1}{2}$$ and a – 2b + c

C. a – 2b + c and  $$\frac{1}{(a + b – 2c)}$$

D. None of the above.

Clearly we see that x=1 satisfies the equation

⇒x=1 is a root of the that equation

Let α be other root

Product of roots =1 × α =  $$\frac{a – 2b + c}{a + b – 2c}$$

other root =  α = $$\frac{a – 2b + c}{a + b – 2c}$$

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### 3 responses to “Nature of Roots”

1. vee kwari says:

how do we state the nature of quadratics

• Karthik says:

A polynomial can have real numbers as zero(ie rational and irrational)to decide it’s nature we can use the relationship between the coefficients and zero (by comparing sum and product of zeroes)