Answer:

Given :-

• If one zero of the polynomial is 5z² + 13z - p is reciprocal of the other.

To Find :-

• What is the value of p.

Formula Used :-

[tex]\clubsuit[/tex] Product Of Zeroes Formula :

[tex]\bigstar \: \: \sf\boxed{\bold{Product\: Of\: Zeroes =\: \dfrac{c}{a}}}\: \: \: \bigstar\\[/tex]

Solution :-

Let,

[tex]\mapsto \bf One\: Zero =\: \alpha[/tex]

[tex]\mapsto \bf Other\: Zero =\: \dfrac{1}{\alpha}[/tex]

Given Equation :

[tex]\bullet \: \: \sf\bold{5z^2 + 13z - p}[/tex]

By comparing with ax² + bx + c = 0, we get :

• a = 5
• b = 13
• c = - p

According to the question by using the formula we get,

[tex]\implies \sf\boxed{\bold{Product\: Of\: Zeroes =\: \dfrac{c}{a}}}\\[/tex]

we have :

• c = - p
• a = 5

So, by putting those values we get,

[tex]\implies \sf \alpha \times \dfrac{1}{\alpha} =\: \dfrac{c}{a}\\[/tex]

[tex]\implies \sf \dfrac{\cancel{\alpha}}{\cancel{\alpha}} =\: \dfrac{- p}{5}\\[/tex]

[tex]\implies \sf \dfrac{1}{1} =\: \dfrac{- p}{5}[/tex]

By doing cross multiplication we get,

[tex]\implies \sf - p \times 1 =\: 5 \times 1[/tex]

[tex]\implies \sf - p =\: 5[/tex]

[tex]\implies \sf p =\: - 5[/tex]

[tex]\implies \sf\bold{\underline{p =\: - 5}}[/tex]

[tex]\therefore[/tex] The value of p is - 5 .