Question

Find the zeroes of polynomial 3x^2-x-4 and verify its relation with zeroes and cofficient

Answer 1

Given,

$the \: quadratic \: polynomial \: is \: 3 {x}^{2} - x - 4.$

$p(x) = 3 {x}^{2} - x - 4$

$3 {x}^{2} - x - 4 = 0$

$3 {x}^{2} - 4x + 3x - 4 = 0$

$x(3x - 4) + 1(3x - 4) = 0$

$(x + 1)(3x - 4) = 0$

$x = - 1 \: and \: \frac{4}{3}$

Therefore the zeros of the polynomial are -1 and 4/3.

Sum of zeros of polynomial = coefficient of x/ coefficient of x^2 = 4/3+(-1)=4/3-1 = 4-3/3=1/3

Product of zeros of polynomial = constant term/coefficient of x^2 = -4/3.

Additional information:

What is a quadratic polynomial?

●A polynomial of degree 2 is called quadratic polynomial.

●More generally,any quadratic polynomial in variable x with the real coefficients is of the form ax^2 + bx + c where a,b and c are real numbers and a is not equal to zero.

●A quadratic polynomial may be a monomial or binomial or a trinomial

Examples: 3x^2-2x+5 and 7x^2-5x+1