Question

write the discriminant of the quadratic equation (x+5)= 2(5x-3)​

Answer 1

${\huge{\boxed{\boxed{\mathcal{QUESTION}}}}}$

Write the discriminant of the quadratic equation

( x + 5 )² = 2( 5x - 3 )

${\huge{\boxed{\boxed{\mathcal{ANSWER\checkmark}}}}}$

★ Concept :

• In these type of questions , first we have to make it a proper quadratic equation .

• The equation should be in the form of :

$\boxed{ \rm \: a {x}^{2} + by + c}$

where , a ≠ 0

• Then we would find it's discriminant .

• Discriminant : It's a quantity , which depends on coefficients of Polynomials and tell the properties of the roots of the Polynomial .

★ Given :

• ( x + 5 )² = 2( 5x - 3 )

★ To Find :

• The Discriminant (d)

★ Solution :

First making it in the form of standard equation .

$\mapsto \rm \: {(x + 5)}^{2} = 2(5x - 3)$

$\mapsto \rm \: {x}^{2} + {5}^{2} + 2 \times x \times 5 = 10x - 6$

$\mapsto \rm \: {x}^{2} + 25 + \cancel{10x} - \cancel{10x} + 6 = 0$

$\mapsto \rm \: {x}^{2} + 31 = 0$

$\implies \boxed{ \rm \: {x}^{2} + 0x + 31 = 0}$

Here ,

$\pink{ \ddot{ \smile} }\: \rm \: a = 1 \\ \blue{ \ddot{ \smile}} \: \rm \: b = 0 \\ \red{ \ddot { \smile}} \: \rm \: c = 31$

So , using the Formula , to find the Discriminant

$\rm \mapsto \: discriminant = {b}^{2} - 4ac$

Put the values now ..

$\mapsto \rm \: d = {0}^{2} + 4 \times 1 \times 31$

$\mapsto \rm \: d = 0 - 124$

$\mapsto \boxed{ \rm \: d = - 124}$

or

$\mapsto \boxed{ \rm \: discriminant = - 124}$

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★ Know more :

• $\rm {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab$
• $\rm \: {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab$
• $\rm \: if \\ \rm \: d > 0 \: \: \: the \: roots \: are \: real \: and \: distinct$
• $\rm \: if \\ \rm \: d = 0 \: \: the \: roots \: are \: real \: and \: equal$
• $\rm \: if \: \\ \rm \: d < 0 \: \: \: \: roots \: are \: imaginary$