Introduction to Quadratic Equations
Any equation of the form ax2 + bx + c = 0 is a quadratic equation, where a, b, and c are real numbers and a is not equal to 0 is called a quadratic equation.
If a and b are the roots for any equation, then (x – a) and (x – b) will be the factors of the equation.
An algebraic expression of the form ax2 + bx + c is called a quadratic function of x.
The graph of a quadratic equation is called a parabola.
The graph of the function f(x) = ax² + bx + c is concave upwards, when a > 0 and concave downwards, when a < 0.
If the graph cuts the xaxis, the roots of the equation will be real and unequal. Their values will be given by the abscissae of the points of intersection of the graph and the xaxis.
If the graph is tangent to the xaxis, the roots are real and equal.
If the graph has no points in common with the xaxis, the roots of the equation are imaginary and cannot be determined from the graph.
The sign of the expression ax² + bx + c is always the same as that of a, except when x lies between or at the roots of ax² + bx + c = 0.
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Q1
The sum of two numbers is 15. If the sum of their reciprocal is 3/10. The two numbers are
Marks:1Answer:
10, 5.
Explanation:
Let two numbers are x and (15x).Then,
So numbers are 5 and 10 or 10 and 5.

Q2
The least value of ax^{2} + bx + c (a > 0) is
Marks:1Answer:
(4ac  b^{2})/4a.
Explanation:
If a > 0 then, ax^{2} + bx + c has a minimum value at x = b/2a and is equal to (4ac  b^{2})/4a.
If a < 0, then ax^{2} + bx + c has a maximum value at x = b/2a and is equal to (4ac  b^{2})/4a.

Q3
The roots of the equation ax^{2} + bx + c = 0 will be reciprocal if
Marks:1Answer:
c = a.
Explanation:
Since roots are reciprocal, product of the roots = 1 c/a = 1 c = a. 
Q4
For a quadratic equation, is one root. The other root must be
Marks:1Answer:
Explanation:

Q5
If p and q are the roots of ax^{2} – 5x + c = 0 such that p + q = pq = 10, then the respective values of a and c are
Marks:1Answer:
(1/2, 5).
Explanation:
Sum of roots (p+q)= (coefficient of x)/coefficient of x^{2}
p + q = (5/a)10 = (5/a)
a = (1/2)
Product of roots(pq) =(coefficient of x)/coefficient of x^{2}
pq=c/a
10=c/(1/2)
10 = 2cc = 5