Advertisements
Advertisements
प्रश्न
Find the zeros of the polynomial `f(x) = x^2 + 7x + 12` and verify the relation between its zeroes and coefficients.
उत्तर
`x^2 + 7x + 12 = 0`
⇒ `x_2 + 4x + 3x + 12 = 0`
⇒ x(x+4) + 3(x+4) = 0
⇒ (x+4) (x+3) = 0
⇒ (x + 4) = 0 or (x + 3) = 0
⇒ x = −4 or x = −3
Sum of zeroes `= -4+(-3)=(-7)/1=(-"Coefficient of " x)/(("Cofficient of " x^2))`
Product of zeroes = `(-4) (-3) =12/1="Constant term"/(("coefficient of " x^2))`
APPEARS IN
संबंधित प्रश्न
The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).
Find the zeroes of the quadratic polynomial `f(x) = x^2 + 3x ˗ 10` and verify the relation between its zeroes and coefficients.
Find the zeroes of the quadratic polynomial `f(x) = 5x^2 ˗ 4 ˗ 8x` and verify the relationship between the zeroes and coefficients of the given polynomial.
Find the zeroes of the polynomial `x^2 – 3x – m(m + 3)`
Find ∝ , β are the zeros of polynomial ∝ +β= 6 and ∝β 4 then write the polynomial.
If the sum of the zeros of the quadratic polynomial `kx^2-3x + 5` is 1 write the value of k..
If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it ______.
If x3 + 1 is divided by x2 + 5, then the possible degree of quotient is ______.
If α and β are the zeroes of the polynomial x2 – 1, then the value of (α + β) is ______.
If α and β are the zeroes of the polynomial x2 + x − 2, then find the value of `alpha/beta+beta/alpha`
