Question

The difference of the two roots of quadratic
equation is 5 and the difference of the square of
the two roots is 85. Write the quadratic equalion
in general fom.​

Answer 1

Answer:

Given:

• $\alpha - \beta = 5$
• $\alpha^2 - \beta^2 = 85$

Solution:

$\alpha ^2 - \beta ^2 = 85$

$\implies(\alpha + \beta)(\alpha - \beta) = 85$

$\implies \alpha + \beta (5) = 85$

$\implies \alpha + \beta = \dfrac{85}{5}$

$\implies \alpha + \beta = 17$

Adding the equations:

$\implies ( \alpha + \beta) + (\alpha - \beta) = 17 + 5$

$\implies 2\alpha = 22$

$\implies \alpha = 11 \ and \ \implies \beta = 6$

$\alpha \beta = 6 \times 11 = 66$

Forming equation:

$x^2 - (\alpha + \beta)x + \alpha \beta = 0$

$\implies x^2 - (17)x + (66) = 0$

$\boxed{\implies{\boxed{x^2 - 17x + 66 = 0}}}$

Answer 2

Answer:

Equation is x^2 -17x +66

Step-by-step explanation:

Let X and Y be the 2 roots.

And let X>Y

So according to question,

X-Y =5................(I)

And X^2 -Y^2 = 85

So, (X+Y)(X-Y) = 85. (identity)

From Eqn (I),

(X+y)(5) =85

Or, X+Y= 17................ (II)

From (I) and (II),

X+Y=5

X-Y=17. (Adding)

--------------

2X=22

Or, X=11, So Y=6

Hence the 2 roots are 11,6

And general form is,

K(x^2 - (x+y)x + xy)

=k(x^2 - 17x + 66)

Putting K=1,

We get the answer!

Plzz...Mark me Branliest!