Relations between Roots of Quadratic Equation
Category : 10th Class
If are the roots of the quadratic equation, then the relation between the roots of the quadratic equation is given by,
Sum of the roots
Product of the roots
Formation of Quadratic Equations
If are the roots of the quadratic equation, S denotes its sum and P denotes its product, then the quadratic equation is given by:
Graphical Representation of a Quadratic Equation
For the quadratic equation , the nature of graph for different values of D is: (a) If D < 0, and a > 0, then the graph is given by:
If a < 0, then the graph is given by.
(b) If D = 0, and a > 0, then the graph of the function is given by
If a < 0, then the graph is given by
(d) If D > 0, and a > 0, then the graph of the function is given by,
If a < 0, then the graph of the function is given by,
Roots of Biquadratic Equation
Any biquadratic equation, , will have four roots. If a, P, Y, and 5 are its roots, then the relation between the roots is given by Sum of the roots
Sum of product of two roots at a time
Sum of product of three roots at a time
Product of the roots
Find the value of.
(a)
(b)
(c)
(d)
(e) None of these
Answer: (a)
Explanation
Let
A If are the roots of the equation, then the value of are.
(a)
(b)
(c)
(d)
(e) None of these
Answer: (b)
Explanation
We have,
If is real and is the roots of , then find the value of .
(a)
(b)
(c)
(d)
(e) None of these
Answer: (d)
Explanation
We have sum of the roots
Product of the roots
Form the above two equations we get,
If are the roots of and are the roots of, then find the value of .
(a) 15
(b) 33
(c) 41
(d) 63
(e) None of these
Answer: (b)
If the coefficient of z in the quadratic equation is taken as 18 in place of 12 and its roots were found to be -16 and -2. The roots of the original equation are:
(a) - 12 & - 6
(b) - 14 & - 4
(c) - 16 & - 2
(d) ? 8 &- 4
(e) None of these
Answer: (d)
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