Quadratic Equation - Signs of the Roots.

Rarely Tested

Signs of the roots: Let P be the product of roots, and S be their sum

P > 0, S > 0 : Both roots are positive
P > 0, S < 0 : Both roots are negative
P < 0, S > 0 : Numerical smaller root is negative, and the other root is positive
P < 0, S < 0 : Numerical larger root is negative, and the other root is positive

Question 1

For how many values of p are the roots of the equation $$(x-p)^{2} + x^{2} = 2$$ are equal and negative?

Question 2

A quadratic equation with roots a and b has 16 as the sum of the roots and -24 as the product. What is the sign of the roots?

Question 3

Find the range of values of k such that the roots of the equation $$x^2 + 2x + k(k+1) = 0$$ are of the same sign.

Name	Date Taken	Score
Formula Test 1	NA	NA
Formula Test 2	NA	NA
Formula Test 3	NA	NA

Not attempted

Not attempted

Not attempted

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