09. Plot the following points on the graph paper. 1 2 3 4 y 5 8 11 14 Join these points. What do you Observe?Do on graph
Answers
Step-by-step explanation:
★QuestioN★:−
Discuss the nature of the roots of the following equations.
\bf{4x^2-12x+9=0}4x
2
−12x+9=0
\pink\bf{\bigstar{AnsweR}\bigstar:-}★AnsweR★:−
✧To find the nature of roots, we have to use the formula for discriminant.
\bf{Discriminant = b^2 - 4ac}Discriminant=b
2
−4ac
✧Here,
:\longrightarrow\green\bf{a=4~,b=-12~, c=9}:⟶a=4 ,b=−12 ,c=9
✧On applying formula,
:\implies\red\bf{b^2-4ac=(-12)^2-4\times4\times9}:⟹b
2
−4ac=(−12)
2
−4×4×9
:\implies\red\bf{144-4\times4\times9}:⟹144−4×4×9
:\implies\red\bf{144-144}:⟹144−144
{\boxed{\underline{\bf{\sf{\red{\bigstar0\bigstar}}}}}
✧Here,
✧D = 0
✧That's why the equation have two equal real roots!!
\huge{\boxed{\underline{\bf{\sf{\red{\bigstar{Extra~Info:-}\bigstar}}}}}
⟿ Nature of roots are based on the discriminant.
⟿ According to that, three types are there. They are,
Two distant real roots.
Two equal real roots.
No real roots.
⟿ Nature of roots of quadratic equations by using quadratic formula,
Two distant real roots if, b² - 4ac > 0.
Two equal real roots if, b² - 4ac = 0
No real roots if, b² - 4ac < 0.
Happy Learning Dear!!♡