Advertisements
Advertisements
प्रश्न
Find the zeroes of the quadratic polynomial x2 + 6x + 8 and verify the relationship between the zeroes and the coefficients.
उत्तर
Given that,
Quadratic polynomial is x2 + 6x + 8
`\implies` x2 + 6x + 8
`\implies` x2 + 4x + 2x + 8
`\implies` x(x + 4) + 2(x + 4)
`\implies` (x + 2)(x + 4)
Zeroes are – 2, – 4
Now, Sum of zeroes = – 2 + (– 4) = – 6
Product of zeroes = (– 2) × (– 4) = 8
Also, Sum of zeroes = `(-b)/a = (-6)/1` = – 6
Product of zeroes = `c/a = 8/1` = 8
Hence, relationship between zeroes and coefficients verified.
संबंधित प्रश्न
Find the zeros of the quadratic polynomial 6x2 - 13x + 6 and verify the relation between the zero and its coefficients.
Find the zeros of the quadratic polynomial 4x2 - 9 and verify the relation between the zeros and its coffiecents.
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
`f(x)=x^2-(sqrt3+1)x+sqrt3`
If If α and β are the zeros of the quadratic polynomial f(x) = x2 – 2x + 3, find a polynomial whose roots are `(alpha-1)/(alpha+1)` , `(beta-1)/(beta+1)`
If α and β are the zeroes of the polynomial f(x) = x2 + px + q, form a polynomial whose zeroes are (α + β)2 and (α − β)2.
Find the quadratic polynomial whose zeroes are `2/3` and `-1/4` Verify the relation between the coefficients and the zeroes of the polynomial.
Find the quadratic polynomial, sum of whose zeroes is `( 5/2 )` and their product is 1. Hence, find the zeroes of the polynomial.
If `x =2/3` and x = -3 are the roots of the quadratic equation `ax^2+2ax+5x ` then find the value of a and b.
If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is –1, then the product of the other two zeroes is ______.
If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then it ______.
