Let x^2-mx+24 be a quadratic with roots x_1 and x_2. if x_1 and x_2 are integers, how many different values of m are possible?

An equation is a statement of equality „=‟ between two expression for particularvalues of the variable. For example5x + 6 = 2, x is the variable (unknown)The equations can be divided into the following two kinds:Conditional Equation:It is an equation in which two algebraic expressions are equal for particularvalue/s of the variable e.g.,a) 2x = 3 is true only for x = 3/2 b) x2 + x –  6 = 0 is true only for x = 2, -3 Note: for simplicity a conditional equation is called an equation.Identity:It is an equation which holds good for all value of the variable e.g;a) (a + b) xax + bx is an identity and its two sides are equal for all values of x. b) (x + 3) (x + 4) x2 + 7x + 12 is also an identity which is true for all values of x.For convenience, the symbol „=‟ shall be used both for equation and identity. 1.2 Degree of an Equation:The degree of an equation is the highest sum of powers of the variables in one of theterm of the equation. For example2x + 5 = 0 1st degree equation in single variable3x + 7y = 8 1st degree equation in two variables2x2  –  7x + 8 = 0 2nd degree equation in single variable2xy –  7x + 3y = 2 2nd degree equation in two variablesx3  –  2x2 + 7x + 4 = 0 3rd degree equation in single variablex2y + xy + x = 2 3rd degree equation in two variables1.3 Polynomial Equation of Degree n:An equation of the formanxn + an-1xn-1 + + a3x3 + a2x2 + a1x + a0 = 0(1)Where n is a non-negative integer and an, an-1, , a3, a2, a1, a0 are realconstants, is called polynomial equation of degree n. Note that the degree of theequation in the single variable is the highest power of x which appear in the equation.Thus3x4 + 2x3 + 7 = 0x4 + x3 + x2 + x + 1 = 0 , x4 = 0are all fourth-degree polynomial equations.By the techniques of higher mathematics, it may be shown that nth degree equation ofthe form (1) has exactly n solutions (roots). These roots may be real, complex or amixture of both. Further it may be shown that if such an equation has complex roots,they occur in pairs of conjugates complex numbers. In other words it cannot have anodd number of complex roots.A number of the roots may be equal. Thus all four roots of x4 = 0are equal which are zero, and the four roots of x4  –  2x2 + 1 = 0Comprise two pairs of equal roots (1, 1, -1, -1)

Hello!

the answer is:

the correct option:

b.

why?

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!

Hello!

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

why?

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!