Question

If p and q are the zeros of the polynomial given below, then the values of(p+q) and (pq) are :x2 + 5x + 8​

Answer 1

Solution

Given :-

• Equation, x² + 5x + 8 = 0
• p & q are zeroes of this equation

Find:-

• Value of (p+q) & p.q

Explanation

Using Formula

★ Sum of zeros = -(Coefficient of x)/(Coefficient of x²)

★ Product of zeroes = (Constant part )/(Coefficient of x²)

So,

==> Sum of zeros = -(5)/1

==> p + q = -5 -------------Equ(1)

And,

==> Product of zeroes = 8/1

==> p.q = 8 ----------------Equ(2)

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Verification of Answer

First calculate zeros of this equation by, Dharacharya Formula

★ x = [-b ± √{b²-4ac}]/2a

Where,

• a = 1
• b = 5
• c = 8

So,

==> x = [ -5 ± √(5²-4*1*8)]/2*1

==>x = [ -5 ± √(25-32)]/2

==> x = [-5 ± √(-7)]/2

==> x = (-5 ± i√7)/2

First take (+ve) Sign

==> x = [-5+√(-7)]/2

==> x = (-5+ i √7)/2

Again, take (-ve) Sign

==> x = [-5-√(-7)]/2

==> x = (-5- i √7)/2

.

Hence

• zeroes ot this equation be = (-5+ i √7)/2 & (-5- i √7)/2

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Now,

==> Sum of zeroes = (-5+ i √7)/2 + (-5- i √7)/2

==> Sum of zeroes = -10/2

==> Sum of zeroes = -5

[ Here, p & q are zeroes ]

==> p + q = -5

Again,

==> product of zeroes = (-5+ i √7)/2 * (-5- i √7)/2

==> product of zeroes = [(-5)² - (i √7)²]/4

==> product of zeroes = [25 - i² * 7 ]/4

==> product of zeroes = [25 -1 * (-1) * 7]/4

==> product of zeroes = (25 + 7)/4

==> product of zeroes = 32/4

==> product of zeroes = 8

[ Here, p & q are zeroes ]

==> p.q = 8

That's proved.

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