Question

If the product of the zeroes of the quadratic polynomial 3x^2=5x+k is -2/3, then​

Answer 1

Answer:  k=2

Step-by-step explanation:

In the given polynomial, $3x^{2}=5x+k$ ⇒ $3x^{2}-5x-k=0$

$a=3,b=-5,c=-k$

Relationship between zeroes and coefficient of the polynomial:

Product of the zeroes =  $\frac{Coefficient of x^2} {Constant term}$$= \frac{c}{a}$

​

$=-2/3$    (given)

from the polynomial,$\frac{c}{a}=\frac{-k}{3}$

                                   $=\frac{-2}{3}=\frac{-k}{3}$

                              ∴$k=2$

Quadratic Equation's Roots

• The values of x that fulfil the quadratic equation $ax^2 + bx + c = 0$ are referred to as the equation's roots.
• They are the values of the variable (x) that the equation requires.
• The x-coordinates of the x-intercepts of a quadratic function are the roots of the function.
• A quadratic equation can only have a maximum of two roots because its degree is 2.
• We can use a variety of techniques to locate the roots of quadratic equations.

Factoring (where possible) (when possible)

Quadratic Equation

• the square graphing is finished (used to find only real roots)
• Let's learn more about the nature of the roots, their discriminant, their sum, and their product as they relate to the quadratic equation.

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