Quadratic Equations

If p and q are the roots of the equation x^2 + px + q = 0

If p and q are the roots of the equation x² + px + q = 0, then

p = 1, q = -2
p = -2, q = 1
p = -2, q = 0
p = 0, q = 1

If a and b are the roots of the equation x^2 - x + 1 = 0

If a and b are the roots of the equation x² - x + 1 = 0, then a²⁰⁰⁹ + b²⁰⁰⁹ is equal to

-2
2
-1
1

The equation e^sinx – e^-sinx – 4 = 0 has

Infinite number of real roots
No real roots
Exactly one real root
Exactly four real roots

Let two numbers have arithmetic mean 9 and geometric mean 4

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

x² + 18x + 16 = 0
x² - 18x - 16 = 0
x² - 18x + 16 = 0
x² + 18x - 16 = 0

A man saves Rs. 200 in each of the first three months of his service

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after

18 months
19 months
20 months
21 months

If α ≠ β but α^2 = 5α - 3 and β^2 = 5β - 3, then the equation having

If α ≠ β but α² = 5α - 3 and β² = 5β - 3, then the equation having α/β and β/α as its roots is

3x² - 19x - 3 = 0
3x² - 19x + 3 = 0
x² - 5x + 3 = 0
3x² + 19x - 3 = 0

Let a and b be roots of the equation px^2 + qx + r, p ≠ 0

Let a and b be roots of the equation px² + qx + r, p ≠ 0. If p, q, r are in A.P. and 1/a + 1/b = 4, then the value of |a - b| is

2√17 / 9
√61 / 9
√34 / 9
2√13 / 9

If a, b, c are distinct +ve real numbers and a^2 + b^2 + c^2 = 1

If a, b, c are distinct +ve real numbers and a² + b² + c² = 1, then ab + bc + ca is

greater than 1
equal to 1
less than 1
any real number

If (1 – p) is a root of quadratic equation x2 + px + (1 – p) = 0

If (1 – p) is a root of quadratic equation x² + px + (1 – p) = 0, then its roots are

0, -1
1, 1
0, 1
2, 1

What is the sum of the squares of the roots of the equation x^2 + 2x - 143 = 0

What is the sum of the squares of the roots of the equation x² + 2x - 143 = 0?

If the difference between the roots of ax^2 + bx + c = 0 is 1

If the difference between the roots of ax² + bx + c = 0 is 1, then which one of the following is correct?

b² = a(a + 4c)
a² = b(b + 4c)
a² = c(a + 4c)
b² = a(b + 4c)

If α and β are the roots of the equation x^2 - q(1+x) - r = 0, then what is (1+α)(1+β)

If α and β are the roots of the equation x² - q(1+x) - r = 0, then what is (1+α)(1+β) equal to?

1 - r
q - r
1 + r
q + r