If p and q are roots of the equation x2 + px – q = 0, then find p and q.
Answers
Answer:
The values of p and q hence found are p = 1, and q = 0. This makes the original equation x^2 - x = 0.
Answer :
p = -1 and q = 2
Step-by-step explanation :
➤ Quadratic Polynomials :
✯ It is a polynomial of degree 2
✯ General form :
ax² + bx + c = 0
✯ Determinant, D = b² - 4ac
✯ Based on the value of Determinant, we can define the nature of roots.
D > 0 ; real and unequal roots
D = 0 ; real and equal roots
D < 0 ; no real roots i.e., imaginary
✯ Relationship between zeroes and coefficients :
✩ Sum of zeroes = -b/a
✩ Product of zeroes = c/a
________________________________
Given quadratic equation,
x² + px - q = 0
It is of the form ax² + bx + c = 0
a = 1 , b = p , c = -q
we know,
⇒ Sum of the roots = -b/a
p + q = -p/1
p + q = -p
p + p = -q
2p = -q
q = -2p
⇒ Product of the roots = c/a
pq = -q/1
pq = -q
p = -q/q
p = -1
q = -2p
q = -2(-1)
q = 2
Therefore,
p = -1 and q = 2