Question

if m and n are the roots of this quadratic equation x²+2x-8=0 and the roots of x²+10x-16p=0 are 3mand 4nrhen what is the value of p

Answer 1

$we \: know \: from \:first \: polynomial \\ m \times n = - 8$
$from \: second \: polynomial \\ 3m \times 4n = - 16p \\ p = \frac{12 \times m \times n}{ - 16} = \frac{12 \times - 8}{ - 16} = 6$

Answer 2

Answer:

Concept :

Any equation in algebra that may be transformed into standard form is known as a quadratic equation. The terms "quadratic coefficient," "linear coefficient," and "constant or free term" can be used to distinguish the three values that make up the equation's coefficients, respectively. Solutions of the equation and roots or zeros of the expression on its left-hand side are the values of x that satisfy the equation. If there is just one solution, it is considered to be a double root. If every coefficient is a real number, there are two real solutions, one real double root, one real triple root, or two complex solutions. When complex roots are taken into account, a quadratic equation always has two roots, and a double root counts as two.

Step-by-step explanation:

Given :

$x^{2}$ + 2x - 8 = 0

$x^{2}$ + 10x -16p = 0

3m and 4n

To find :

Value of p

Solution :

From first quadratic equation,

m × n = -8

Second quadratic equation,

3m × 4n = -16p

p = 12×m×n/-16

p = 12×-8/-16

p =  $\frac{-96}{-16}$

p = 6.

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