Let λ be a real number for which the system of linear equations $$x+y+z=6$$,$$4x+$$λy−λ$$z=$$λ−$$2and$$ $$3x+2y$$−$$4z=$$−$$5$$ has infinitely many solutions . Then is a root of the quadratic equation

Question

Let λ  be a real number for which the system of linear equations  $$x+y+z=6$$,$$4x+$$λy−λ$$z=$$λ−$$2and$$  $$3x+2y$$−$$4z=$$−$$5$$ has infinitely many solutions . Then   is a root of the quadratic equation

Infinity Learn · Accepted Answer

Given, system of linear equations $$x+y+z=64x+$$λy−λ$$z=$$λ−$$2$$ And  $$3x+2y$$−$$4z=$$−$$5$$ Has infinitely manv solutions then Δ$$=0$$⇒$$1114$$λ−λ$$32$$−$$4=0$$⇒$$1($$−$$4$$λ$$+2$$λ$$)$$−$$1($$−$$16+3$$λ$$)+1(8$$−$$3$$λ$$)=0$$⇒−$$8$$λ$$+24=0$$⇒λ$$=3$$ From the options λ$$=3$$. satisfy the quadratic equation λ$$2$$−λ−$$6=0$$

Let $λ$ be a real number for which the system of linear equations $x + y + z = 6, 4 x + λ y - λ z = λ - 2$ and $3 x + 2 y - 4 z = - 5$ has infinitely many solutions . Then is a root of the quadratic equation

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Let λ be a real number for which the system of linear equations x+y+z=6,4x+λy−λz=λ−2and 3x+2y−4z=−5 has infinitely many solutions . Then is a root of the quadratic equation

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Let $λ$ be a real number for which the system of linear equations $x + y + z = 6, 4 x + λ y - λ z = λ - 2$ and $3 x + 2 y - 4 z = - 5$ has infinitely many solutions . Then is a root of the quadratic equation