Advertisements
Advertisements
प्रश्न
If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then ______.
पर्याय
c and a have opposite signs
c and b have opposite signs
c and a have the same sign
c and b have the same sign
Advertisements
उत्तर
If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then c and a have the same sign.
Explanation:
The zeroes of the given quadratic polynomial ax2 + bx + c where c ≠ 0, are equal.
If coefficient of x2 and constant term have the same sign i.e. c and a have the same sign.
While b i.e., coefficient of x can be positive or negative but not zero.
Consider,
(i) x2 + 4x + 4 = 0
`\implies` (x + 2)2 = 0
`\implies` x = –2, –2
(ii) x2 – 4x + 4 = 0
`\implies` (x – 2)2 = 0
`\implies` x = 2, 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).
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 polynomial `f(x) = x^2 ˗ 2x ˗ 8` and verify the relation between its zeroes and coefficients
Obtain all other zeroes of `(x^4 + 4x^3 – 2x^2 – 20x – 15)` if two of its zeroes are `sqrt5 and –sqrt5.`
Find all the zeroes of polynomial `(2x^4 – 11x^3 + 7x^2 + 13x – 7)`, it being given that two of its zeroes are `(3 + sqrt2) and (3 – sqrt2)`.
If one zero of the polynomial `x^2-4x+1 is (2+sqrt3)` , write the other zero.
Find ∝ , β are the zeros of polynomial ∝ +β= 6 and ∝β 4 then write the polynomial.
If 3 is a zero of the polynomial `2x^2 + x + k`, find the value of k.
If one zero of the quadratic polynomial `kx^2 + 3x + k is 2`, then find the value of k.
If -4 is a zero of the polynomial `x^2 – x – (2k + 2) is –4`, then find the value of k.
If the sum of the zeros of the quadratic polynomial `kx^2-3x + 5` is 1 write the value of k..
If ∝ and β are the zeros of the polynomial f(x) = `6x^2 + x - 2 `find the value of `(∝/β+∝/β) `
If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it ______.
A quadratic polynomial, whose zeores are -4 and -5, is ______.
If p(x) is a polynomial of at least degree one and p(k) = 0, then k is known as ______.
If 4x² – 6x – m is divisible by x – 3, the value of m is exact divisor of ______.
The zeroes of the quadratic polynomial x2 + kx + k, k ≠ 0 ______.
The number of quadratic polynomials having zeroes –5 and –3 is ______.
The graph of y = f(x) is shown in the figure for some polynomial f(x).
The number of zeroes of f(x) is ______.
