Question

If truth and lie are zeroes of the polynomial px2
+ qx + r, (p  0) and zeroes are
reciprocal to each other,
(i) Find the relation between p and r. (ii) Which value do you learn from this question?

Answer 1

Truth and lie are zeros of the polynomial Px² + qx + r , ( P ≠ 0) ,.and zeros are reciprocal to each other . Means truth = 1/lie or, truth.lie = 1

Use product of zeros = constant/coefficient of x²
Truth.lie = r/p
1 = P/r ⇒ P = r

Hence, relation between p and r : P = r

Now put P = r in given equation
rx² + qx + r = 0
Discriminant , D = b² - 4ac = q² - 4r.r
D = q² - 4r²
When zeros is real , D ≥ 0
q² ≥ 4r² , hence for real value q² must be greater than equal to 4r² .

Answer 2

Answer:

Truth and lie are zeros of the polynomial Px² + qx + r , ( P ≠ 0) ,.and zeros are reciprocal to each other . Means truth = 1/lie or, truth.lie = 1

Use product of zeros = constant/coefficient of x²

Truth.lie = r/p

1 = P/r ⇒ P = r

Hence, relation between p and r : P = r

Now put P = r in given equation

rx² + qx + r = 0

Discriminant , D = b² - 4ac = q² - 4r.r

D = q² - 4r²

When zeros is real , D ≥ 0

q² ≥ 4r² , hence for real value q² must be greater than equal to 4r² .