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
From the quadratic equations, whose roots are and | |||
Right Option : A | |||
View Explanation |
If and are the zeroes of the quadratic polynomial , find the value of | |||
Right Option : B | |||
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 |
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