Relationship of Zeroes With Coefficients of Quadratic Polynomial
Relationship of Zeroes With Coefficients of Quadratic Polynomial
Relationship of Zeroes With Coefficients Of Quadratic Polynomial:
If (read as alpha) is a zero of p(x) then
If and
( read as beta) are two zeroes of p(x) then
We can use these reltaions to obtain values of several symmetric expressions involving and
in terms of a, b and c.
An expressons in and
is said to be symmetric if it remaiins unchanged when
and
are intercharged. For instance,
and
are symmetric expressions in
and
.
Example: If a and c are such that the quadratic polynomial has 10 as the sum of zeroes and also as the product of zeroes, fiind a and c.
Solution: Let be the zeroes of
Then
As we get
and c = 10a = 5
Thus,
Example : If and
are zeros of the quadratic polynomial
. find the value of
Solution:
We first find We have
Next
Thus,
Example: If are zeros of
then obtain quadratic polynomials whose zeros are
Solution: As are zeros of
Thus, the quadratic expression whose zeros are is
or
or
If
| |||
| Right Option : D | |||
| View Explanation | |||
A and B solve a quadratic equation. In solving it, A made a mistake in the constant term and obtained the roots as 5, -3, while B made a mistake in the coefficient of x ans obtained the roots as -1, 3. The correct roots of the equation are : | |||
| Right Option : B | |||
| View Explanation | |||
Quadratic equation whose one of the roots is | |||
| Right Option : D | |||
| View Explanation | |||
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