[tex]\bold{\huge{\underline{ Solution }}}[/tex]
• Quadratic equation is defined as the equation having highest power of degree as 2 .
• The general form of quadratic equation is ax² + bx + c
• Generally, we solve quadratic equations by factorization method but it not applicable for two quadratic equations.
• Factorization method is also applicable for linear, cubic etc.
• When we have two different types of quadratic equations then we use substitution method, elimination method and cross multiplication method.
• Factorization method is also known as middle term splitting method.
Here, we have equation
By using factorisation method
[ Here, we have taken 3 and 7 because "7 + 3 = 10 " and " 7 × 3 = 21 ]
[tex]\sf{ x( x + 3) + 7( x + 3 )}[/tex]
[tex]\sf{ ( x + 3 ) ( x + 7) }[/tex]
Hence, The required answer is
(x + 3)(x + 7) .
Here ,we have equation
By using factorisation method,
[ Here, we have taken 4 and 4 because "4 + 4 = 8 " and " 4 × 4 = 16 ]
[tex]\sf{ a( a + 4) + 4( a + 4) }[/tex]
[tex]\sf{ ( a + 4) ( a + 4) }[/tex]
Hence, The required answer is
( a + 4)( a + 4) .
Here, we have equation ,
By using factorisation method,
[ Here, we have taken - 5 and -5 because "-5 + (-5) = -5 - 5 = - 10 " and " -5 × -5 = 25]
[tex]\sf{ p( p - 5) - 5(p - 5) }[/tex]
[tex]\sf{ ( p - 5) (p - 5) }[/tex]
Hence, The required answer is
(p - 5)( p - 5) .
Here, we have equation
By using factorisation method ,
[ Here, we have taken -4 and -3 because "- 4 + (- 3) = -4 - 3 = - 7 " and " -4 × -3 = 12]
[tex]\sf{ y( y - 4 ) - 3 ( y - 4 ) }[/tex]
[tex]\sf{ ( y - 3) ( y - 4) }[/tex]
Hence, The required answer is
(y - 3)( y - 4) .
