Question

if α and β are the zeros of the quadratic polynomial f(x) = 2x2 – 5x + 7, then find α/β+β/α

Answer 1

Question :-

if α and β are the zeros of the quadratic polynomial f(x) = 2x2 – 5x + 7, then find α/β+β/α.

Solution :-

Given Quadratic Equation :

• 2x² - 5x + 7

When the quadratic equation x² have a numerical and we have to factories it then multiply then numerical with c. Mean that the last number.

We get,

$\sf: \longmapsto{x {}^{2} - 5x + 14 }$

Factories the Quadratic equation by splitting the middle term

$\sf: \longmapsto{x {}^{2} - 5x + 14 = 0} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf: \longmapsto{x {}^{2} - 7x + 2x + 14 = 0 } \: \: \: \\ \\ \sf: \longmapsto{x(x - 7) + 2(x - 7) = 0} \\ \\ \sf: \longmapsto{(x - 7 )(x + 2) = 0} \: \: \: \: \: \: \: \: \: \\ \\ \sf: \longmapsto{x - 7 = 0} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \bf: \longmapsto \red{x = 7} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf: \longmapsto{x + 2 = 0} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \bf: \longmapsto \red{x = - 2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

We got α and β.

$\rm :\longmapsto{ \alpha = 7} \: \: \: \: \\ \\ \rm :\longmapsto{ \beta = - 2}$

We Need to find :

$\rm :\longmapsto{ \frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } }$

On substituting values we get,

$\sf :\longmapsto{ \frac{7}{ - 2} + \frac{ - 2}{7} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf :\longmapsto{ \frac{(7 \times 7) + ( - 2 \times - 2)}{ - 2 \times 7} } \\ \\ \sf :\longmapsto{ \frac{49 + 4}{ - 14} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf :\longmapsto{ \frac{53}{ - 14} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence,

$\red \bigstar \: \: { \boxed{ \sf{ \frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } = \frac{53}{ - 14} }}}$

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Learn more from brainly :

If α and β are the zeroes of the quadratic polynomial f(x)=ax2+bx+c

then evaluate,a(α²/β+β²/α)+b(α/β+β/α).

https://brainly.in/question/16537882

Answer 2

Answer:

This might help you

Step-by-step explanation:

a+b= 5/2

ab=7/2

a/b+b/a = a+b/ab = 5/2/7/2=5/7