Advertisements
Advertisements
Question
Find the zeroes of the quadratic polynomial `(3x^2 ˗ x ˗ 4)` and verify the relation between the zeroes and the coefficients.
Solution
`3x^2 ˗ x ˗ 4 = 0`
`⇒3x^2 ˗ 4x + 3x ˗ 4 = 0`
`⇒x (3x ˗ 4) + 1 (3x ˗ 4) = 0`
`⇒(3x ˗ 4) (x + 1) = 0`
`⇒ (3x ˗ 4) or (x + 1) = 0`
`⇒x=4/3 or x=-1`
Sum of zeroes `4/3+(-1)=1/3=(-("Coefficient of x"))/(("Coefficient of x"^2))`
Product of zeroes =`4/3xx(-1)=(-4)/3=("Constant term") /(("Coefficient of "x^2))`
APPEARS IN
RELATED QUESTIONS
Verify that the numbers given along side of the cubic polynomials are their zeroes. Also verify the relationship between the zeroes and the coefficients.
`2x^3 + x^2 – 5x + 2 ; 1/2, 1, – 2`
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
`q(x)=sqrt3x^2+10x+7sqrt3`
If the zeros of the polynomial f(x) = 2x3 − 15x2 + 37x − 30 are in A.P., find them.
Find the condition that the zeros of the polynomial f(x) = x3 + 3px2 + 3qx + r may be in A.P.
By actual division, show that x2 – 3 is a factor of` 2x^4 + 3x^3 – 2x^2 – 9x – 12.`
Find all the zeroes of `(x^4 + x^3 – 23x^2 – 3x + 60)`, if it is given that two of its zeroes are `sqrt3 and –sqrt3`.
If two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are each equal to zero, then the third zero is
What should be added to the polynomial x2 − 5x + 4, so that 3 is the zero of the resulting polynomial?
If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.
If α, β are zeroes of quadratic polynomial 5x2 + 5x + 1, find the value of α2 + β2.
