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), in the following.
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 zeros of the polynomial `f(x) = x^2 + 7x + 12` 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.
One zero of the polynomial `3x^3+16x^2 +15x-18 is 2/3` . Find the other zeros of the polynomial.
If 3 is a zero of the polynomial `2x^2 + x + k`, find 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) `
Find the value of k such that the polynomial x2 − (k + 6)x + 2(2k −1) has sum of its zeros equal to half of their product.
If one zero of the quadratic polynomial x2 + 3x + k is 2, then the value of k is ______.
If one of the zeroes of the quadratic polynomial (k – 1) x2 + kx + 1 is - 3, then the value of k is ______.
A quadratic polynomial, whose zeroes are -3 and 4, is ______.
If the zeroes of the quadratic polynomial x2 + (a + 1) x + b are 2 and –3, then ______.
The number of polynomials having zeroes as -2 and 5 is ______.
If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is -1, then the product of the
other two zeroes is ______.
The zeroes of the quadratic polynomial x2 + 99x + 127 are ______.
If the zeroes of the quadratic polynomial ax² + bx + c, c # 0 are equal, then ______.
If x3 + 1 is divided by x2 + 5, then the possible degree of quotient is ______.
A polynomial of degree n has ______.
The number of polynomials having zeroes – 3 and 4 is ______.
The given linear polynomial y = f(x) has
