Question

if the sum of squares of roots of x square + p x minus 3 is equal to zero is 10 then P is ​

Answer 1

Answer:

p = ± 2

Step-by-step explanation:

Let the roots of the given polynomial be α and β.

f(x) = x² + px - 3

On comparing this with ax² + bx + c, we get

a = 1, b = p, c = - 3

Now,

• Sum of zeroes = α + β = - b/a

→ α + β = - p/1

→ α + β = - p

• Product of zeroes = αβ = c/a

→ αβ = - 3/1

→ αβ = - 3

A.T.Q.,

→ α² + β² = 10

{ Identity : (a + b)² = a² + b² + 2ab

From this, we get [ a² + b² = (a + b)² - 2ab ]

Here, a = α, b = β }

We can write this as :

→ (α + β)² - 2αβ = 10

Putting known values, we get

→ (- p)² - 2(- 3) = 10

→ p² + 6 = 10

→ p² = 10 - 6

→ p = √4

→ p = ± 2

Answer 2

AnswEr :

p = 2

$\bf{\large{\underline{\underline{\mathfrak{Given\::}}}}}}$

If the sum of Quadratic polynomial of roots x² + px - 3 = 0 is 10.

$\bf{\large{\underline{\underline{\mathfrak{To\:fiNd\::}}}}}}$

The value of p.

$\bf{\large{\underline{\underline{\tt{\green{Explanation\::}}}}}}$

Let the roots α and β

We have, x² + px - 3

We compared by the equation are Ax² + Bx + C.

• A = 1
• B = p
• C = -3

$\bf{\large{\underline{\underline{\tt{\red{A.T.Q.\::}}}}}}$

$\leadsto\tt{\alpha ^{2} +\beta ^{2} =10}$

$\bf{\large{\underline{\underline{\tt{\green{\bigstar{Sum\:of\:RooTs\::}}}}}}}$

$\dashrightarrow\tt{\alpha +\beta =-\dfrac{B}{A} }\\\\\\\dashrightarrow\tt{\alpha +\beta =-\dfrac{p}{1} }\\\\\\\dashrightarrow\tt{\red{\alpha +\beta =-p}}$

$\bf{\large{\underline{\underline{\tt{\green{\bigstar{ProducT\:of\:RooTs\::}}}}}}}$

$\dashrightarrow\tt{\alpha \times \beta =\dfrac{C}{A} }\\\\\\\dashrightarrow\tt{\alpha \times\beta =\dfrac{-3}{1} }\\\\\\\dashrightarrow\tt{\red{\alpha \times \beta =-3}}$

Now,

$\longrightarrow\tt{(\alpha +\beta )^{2} =\alpha ^{2} +\beta ^{2} +2\alpha \beta }\\\\\\\\\longrightarrow\tt{(-p)^{2} \:=\:10+2(-3)}\\\\\\\\\longrightarrow\tt{(-p)^{2} \:=\:10+(-6)}\\\\\\\\\longrightarrow\tt{(-p)^{2} \:=\:10-6}\\\\\\\\\longrightarrow\tt{(-p)^{2} =4}\\\\\\\\\longrightarrow\tt{p\:=\:\sqrt{4} }\\\\\\\\\longrightarrow\tt{\red{p\:=\:2}}$

∴ The value of p is 2.